For the countries of the former Warsaw Pact borders were normally restricted to permitted traffic. Borders themselves were patrolled and places where one could cross it were limited. Mind you that permission to cross the border was not only for the "entering another country" part, one had to have permission to be able to leave one's home country, too. Different countries did it differently in different time periods
For example, Poland issued in 1970-1990 period, besides customary and internationally recognized passports (which were issued on "per travel basis" and had to be turned back over to authorities upon return), also something called
passport insert, which contained entry that owner could cross the state border, and it was valid with one's ID only, and just for a number of socialist countries. In later time of that period that
insert was replaced by an entry in the ID (stamp, as @MarkJohnson pointed out), but it was still for the "demopeoples'.
In case of the Polish-Czechoslovakian border, it was yet another difference.
In 1955 both states signed a
Polish-Czechoslovakian Tourism Convention, which designated a number border regions (expanded in 1961-62 to several more, including ones with road border crossings), where passport-less traffic was permitted and where only a
pass was required. However, the border could be crossed only at designated points, but my understanding was that there was a lot of them and at popular tourist foot trail traffic especially.
In 1959 there was additional agreement about "small cross-border traffic", that defined a zone at the border where dwellers were entitled to receive a
pass authorizing crossing (difference between 1955 and this one was former was tourism-oriented, while latter expanded reasons to receive the
pass to a number of them i.e. work, family etc.)
In 1986 there was another agreement signed, but it formalized organized tourism and had no impact on the cross-border traffic.
The change came in 1991, when another treaty abolished visa requirement.
All those were carried over when Czechoslovakia first reformed internally and then split. Some of them are still in force.
In 1995 there was another treaty about "small cross-border traffic", this time between Poland and Czechia and Poland and Slovakia, requiring only ID for dwellers of the defined border zone instead of passports.
After joining EU and Schengen there are no more restrictions on cross border traffic.
I have no information if these were suspended temporarily after both 1968 Czechoslovakian Uprising nor 1980s Polish unrests.
From my personal experience the tourism up until 2006 was not hampered, but of course passports were required whenever crossing borders were required. Snezka is one example but Biskupská Kupa (PL: Kopa Biskupia) is actually hilarious one: the area is very attractive and active tourism region. And when I was there in 2003, I had to present a document to traverse 200m path from PL-CZ border to the actual viewpoint, located at the top of that mountain. It was just ID for me, but friend from different town had no passport, so he had to wait. Fortunately those times are gone...
Passport: official document issued for the purpose of confirmation of holder's identity and nationality.
Pass: document issued by any authorized official confirming holder's right to enter and move within any restricted area. In case of this question the pass could be in the form of paper document to be presented with ID or - in Poland at least - suitable entry in the ID (usually a stamp).
Polish ID document before 2001 was a multi-page document very similar in appearance to international passports.