That is a great question and something I have not thought about. The large mammal I know of that hibernates - northern bears (meaning grizzly, polar, etc) - do not hibernate in zoos because they are fed throughout the winter. If the zoo is open in winter obviously it would negatively affect their visitor numbers to have key animals hibernating.
I'm sure I've read that the brown bears at Helsinki and Orsa Bjornpark do hibernate. Maybe this is the norm for Scandinavian zoos?
For one thing, brown bears do not hibernate , but I know from several zoos in Switzerland and the Netherlands that they let them have their winter nap. A very effective tool to let reptiles/ampbibians hibernate is the Fridge, not very fancy but it works.
I believe there have been several outdoor displays of native reptiles and amphibians here in the UK which have incorporated suitable hibernation sites. I think Paignton used to have an off-show facility for Hazel Dormouse which must have had hibernation sites - as these would just be the same boxes used in field conservation provision they would be simple to provide. Actually, this whole question is bigger than just hibernation for temperate zone animals - many species have reproduction and other behaviours keyed to seasonal changes in day length/ rainfall/ diet/ temperature etc and duplicating this in captivity may need more attention than it often receives.
I've heard of Skansen in Stockholm also having winter sleeping brown bears and I know for sure that Polar Park's (Norway) brown bears deep sleep in winter, but occasionally wake up for snacks.
Taronga Zoo has mountain pygmy possums which they keep in a refrigerated off-show building during hibernation months. Each one has a box where they hibernate and the temperature had to be kept the same as in the wild.
In Denmark, the brown bears in year-round-open city zoos Aalborg and Copenhagen don't hibernate - then again, Denmark is also the southernmost part of Scandinavia and doesn't have any bears in the wild. The brown bears of Skandinavisk Dyrepark do hibernate, though - probably because that zoo closes for the winter, and maybe also because the bears there have a much bigger and more natural exhibit than the ones in Aalborg and Copenhagen.
There are a few European zoos which keep Black-tailed prairie dogs in outdoor enclosures all year round. Do they hibernate? There is at least one small swiss zoo, which keeps Edible dormouse.
Brown bear hibernation largely depends on temperature and food. As a consequence, wild brown's in the coldest regions hibernate far longer than others and some southern only partially (i.e., some individuals don't and the ones that do only for a quite short period). A famous example of the partial hibernators are the ones on Kodiak Island where winters are milder than much of mainland Alaska. Overall brown's are also considered "light hibernators", unlike many e.g. rodents and bats. BTW, wild brown's did live in Denmark in the Stone Age, disappearing about the time when the Bronze Age started in Scandinavia a few thousand years ago. They lived there both during times where the climate was slightly colder than today, directly after the last Ice Age, and when it was slightly warmer (average 2-3°C warmer).
