The evidence for this is weak, but interesting and indicative of "on a much smaller scale", but not "as well" as in equally transformative:
From East to West:
They introduced the mouse to the American continent. For sure, if we accept Greenland and Iceland as part of that continent, unsure if we only count Newfoundland:
House mice samples from Iceland, whether from archaeological Viking Age material or from modern-day specimens, had an identical mtDNA haplotype to the clade previously linked with Norwegian Vikings. From mtDNA and microsatellite data, the modern-day Icelandic mice also share the low genetic diversity shown by their human hosts on Iceland. Viking Age mice from Greenland had an mtDNA haplotype deriving from the Icelandic haplotype, but the modern-day Greenlandic mice belong to an entirely different mtDNA clade. We found no genetic association between modern Newfoundland mice and the Icelandic/ancient Greenlandic mice (no ancient Newfoundland mice were available). The modern day Icelandic and Newfoundland mice belong to the subspecies M. m. domesticus, the Greenlandic mice to M. m. musculus.
In the North Atlantic region, human settlement history over a thousand years is reflected remarkably by the mtDNA phylogeny of house mice. In Iceland, the mtDNA data show the arrival and continuity of the house mouse population to the present day, while in Greenland the data suggest the arrival, subsequent extinction and recolonization of house mice - in both places mirroring the history of the European human host populations. If house mice arrived in Newfoundland with the Viking settlers at all, then, like the humans, their presence was also fleeting and left no genetic trace. The continuity of mtDNA haplotype in Iceland over 1000 years illustrates that mtDNA can retain the signature of the ancestral house mouse founders. We also show that, in terms of genetic variability, house mouse populations may also track their host human populations.
EP Jones et al.: "Fellow travellers: a concordance of colonization patterns between mice and men in the North Atlantic region", BMC Evolutionary Biology, 2012, 12:35, DOI.
Then there is evidence for livestock, in this case cattle:
The expedition did not stop due to Thorstein’s death. Thorfinn Karlsefni fell in love with Thorstein’s newly widowed wife, Gudrid. The pair rekindled talks of expedition and Thorfinn took Thorstein’s place as the leader. Thorfinn sailed with “sixty men and five women,” and “took livestock of all kinds, for they intended to make a permanent settlement.” This is a significantly larger expedition than any prior expedition. In the first summer, Indigenous people came to the colony. Thorfinn, frightened, locked the gates, but the Indigenous group was able to convince him to trade. When they “saw the milk they wanted to buy nothing else.” The two groups traded milk for furs.
Magnus Magnusson & Hermann Pálsson (eds.): "The Vinland Sagas: Grænlendinga Saga and Eirik's Saga", New York University Press, 1966, p57.
Brigitta Wallace notes that the storage spaces at L’Anse aux Meadows was unusually large for a Norse settlement, and that indicates that it is “a place where goods were collected.” But just no remains of specialised buildings for livestock. This doesn't rule out animals living with humans in the same house or specialised buildings elsewhere. Or just that
The observed effect of these recent fluctuations suggests that winters at L'Anse aux Meadows in the eleventh century were likely snowless and that cattle could indeed have grazed out of doors all winter.
Birgitta Wallace: "The Norse in Newfoundland: L'Anse aux Meadows and Vinland", Newfoundland and Labrador Studies. 19 (1): 5–43.
The L’Anse aux Meadows settlement was intended for year-round occupation as shown in the building construction. All the structures were regular buildings with permanent roofs, not the booths with temporary tent roofs found on seasonally used sites.
Although villages or towns never developed in Greenland or Iceland,20 another characteristic of west-Norse settlements was that a singular farm or estate could not function in isolation. By the time self-sufficient farms were established in Iceland and Greenland, a whole network of settlement was required.
Birgitta Linderoth Wallace: "L’Anse aux Meadows and Winland: An Abandoned Experiment", in: James H. Barrett (Ed): "Contact, Continuity, and Collapse: The Norse Colonization of the North Atlantic", Brepols: Turnhout, 2003, p219.)
If 'exchange' includes trade, then this included all kinds of berries (Vinland) and butternuts from further South. Export of this back to Greenland as a food item is not unlikely; if 'exchange' means bringing species to a new habitat: cultivation of them up North on the other hand is unlikely.
The contact between Norse explorers and settlers with indigenous people lasted for centuries in several small colonies. (Donald E. Warden: "The Extent of Indigenous-Norse Contact and Trade Prior to Columbus" Oglethorpe Journal of Undergraduate Research, Volume 6, Issue 1, August 2016. PDF)
From West to East:
Analyzing a type of DNA passed only from mother to child, scientists found more than 80 living Icelanders with a genetic variation similar to one found mostly in Native Americans.
This signature probably entered Icelandic bloodlines around A.D. 1000, when the first Viking-American Indian child was born, the study authors theorize.
Traci Watson: "American Indian Sailed to Europe With Vikings? ––
Centuries before Columbus, a Viking-Indian child may have been born in Iceland", National Geographic, November 26, 2010. Referencing Sigríður Sunna Ebenesersdóttir et al.: "A new subclade of mtDNA haplogroup C1 found in icelanders: Evidence of pre‐columbian contact?", American Journal of Physical Anthropology, Volume 144, Issue 1, January 2011, Pages 92-99. DOI.
Further, it seems that at least one polar bear (note his natural range) made the way from the Canadian Arctic or at least Greenland via Emperor Frederick to the Sultan of Egypt.
Frederick II’s propensity for exotic wild animals is well documented. Al-Kamil apparently once gave Frederick the gift of an elephant, resuscitating the cultural memory, perhaps, of Harun al-Rashid’s gift of the elephant Abu al-Abbas to that first Holy Roman Emperor, Charlemagne. Frederick arguably topped the Sultan by giving Al-Kamil a polar bear “which to the amazement of the Arabs eats nothing but fish”
Numerous quotes available, but this one from p254 of Geraldine Heng: "The Invention of Race in the European Middle Ages", Cambridge University Press: Cambridge, New York, 2018.
Another was a gift from the King of Norway to Henry the III in 1252.