The normal ballpark estimate of how much heat a person gives off is comparison to a 100W (sometime 120W) incandescent light bulb. The Theater an der Wien had a capacity of 2,000 in Beethoven's time, which was more than sufficient to heat a building in temperatures only near freezing.
Originally, it was “more spacious than any in Vienna”, with a capacity of almost 2,000 whereas today it seats 950.
Even at only 3/4 capacity that is generated heat of 1500 * 100W = 150kW. If the building was reasonably insulated, one might in a normal winter have been more concerned with how to cool the building when at or near capacity.
Typical December temperatures in Vienna are not particularly cold, with typical daily highs around 3C (38F) and overnight lows about -1C (30F). However the winter of 1808/09 was one of the coldest on record across Europe. I coudn't find records specifically for Vienna, but:
At Stockholm [, only] the winters 1788/89 and 1808/09 are found to be colder [than that of 1941/42].
From my comment below:
Theatrical events are typically preceded by 60 minutes or more of meet & greet as patrons enter the building. It can take another 20 minutes after that to seat everyone. And, traditional European formal attire is already intended to keep one warm in temperatures of around 10-12 C; not the 20-22C we normally think of as room temperature.
Observe here, from the Congress of Vienna in 1815, the men's attire for a business meeting. Note the jackets, with stiff high collar on both jacket and blouse to keep out drafts. The reason men today feel so compelled to remove their jacket immediately on entering a building is that our modern room temperature is about 10C warmer than that which the attire is designed for. This is also why the collars have lowered and gotten looser over the past century.
For women, formal dress seems to have always been a bit lighter than for men. However the tradition was that decolletage was for dancing, and every fashionable woman had a stole, preferably ermine if affordable, to keep her shoulders and neckline warm:
Also, Mrs. Willott in a white Stole:
Here, German Biedermeier period fashion, 19th century: