Many estate agents will still be working (except Christmas day and New Year's Eve/Day--no way). You should call in advance. My DH and I saw about 12 rental properties between Christmas and New Year's last year. Although, hoo boy, motivating people to work then is rough. They are in the office, but checked out-mentally. In order to get people to show us stuff, we pretty much acted like we were definitely going to get something ASAP. However, it was enough to convince us that we could move to this city and be happy.
The city we live in is chaos around Christmas-time and boxing day, with all the shoppers coming to town. So, I would note that this season is inordinately crowded in all urban areas, and not necessarily reflective of the rest of the year. Also, you'll be looking during the shortest days of the year, so there won't be much light...
Good luck. It is truly a spectacle to see few people about on Christmas day...