I have visited Woburn Safari Park twice now once last month and before that it was in summer two years ago.
I must say that weather wise it doesn't really matter when you go the animals seem to come out in all conditions. Last month on the day i went, it was absolutely chucking it down so i expected the animals to be seeking refuge in a shelter somewhere so i wouldn't see them. However, i was amazed to find that this made them more active than when i had seen them in the summer time.
There are distinct advantages to seeing them in the Winter.
1. You can actually see them! In the summer it is virtually impossible to get close enough to see them because of the army of cars and 4x4s all lined up in front of where their sitting.

I throughly enjoyed this when i went last month especially as when we went round the Siberian Tigers were being feed a deer carcas.
It was just like seeing it on the telly only better. The animals there are very well cared for and have masses of space. The Siberian tigers were the best for me as they looked like they were truly at home. They even began fighting over the food and at one point about five of them came charging towards the cars and one was stood right next to my window - was terrifying!
The safari drive is long and quite varied however it is not the best safari drive i have been on as there are not as many animals on display as i thought there would be. There claim to be wolves there but both times i have been there i havent seen not even a glimpse of one.
Another interesting part of the drive is the part where you drive through the Patas Monkeys enclosure which was a different experience lol!
I wouldnt recommend this if you have a particulary nice car as the monkeys can be vicious! I now have a broken windscreen wiper as a result of an excitable little monkey!

I was very dissapointed with the restaurant area at Woburn.
There is only one resturant which in the summer time means you almost definately wont get a seat in the small restaurant.
The food is eadable but not the greatest nor is the choice. However the prices are good, very cheap which surprised me as these sort of attractions nearly always overcharge!
I would recommend bringing a pack lunch if you are planning on a visit in the summer!
The toilets and baby changing facilites are average, but thats fine as you dont expect the ritz when you come to a safari park!

Now i was expecting a bit more to do after the safari drive than what is on offer.
There are other animals to see but it should take you no more than an hour so that leaves the day a bit short i found.
I personally didn't see the demonstrations so i cant comment on those. However i do know there are a good variety of talks and demonstrations on a daily basis so they would probably fill up your day.