I visited Chitwan in december, which is the winter time. I had a great stay and thoroughly enjoyed every minute of my time there. However, while staying there i was told by a couple of the local guides that the best time to visit Chitwan is february/march in the spring time.
The weather, although very pleasant while i was there, is just a little warmer in the spring, and predominently dry. Still not too many insects or mosquito's around.
The big advantage though is for viewing the wildlife. At that time of year the locals have been allowed to go into the jungle and cut a lot of the grass down and take home to be used. This gives far better visibilty of the animals as they have much less cover to hide in.
I was told the tharu tribes living in this area have developed malaria resistance, being among the very few people with the particularly interesting feature. But with the eradication of malaria in whole Terai, population numbers have steadily increased, with people heading here from other parts of Nepal to take advantage of the mild climate and agricultural land.
Consider the Tharu show the organisers will prepare for you in one of the nights as one way to support the locals from the nearby villages.
Favorite thing: If going to Chitwan independently, the book "Royal Chitwan National Park in Nepal" by Prakash A: Raj, Nabeen Publications 1995, is a good choice of companion. 65 pages of guidebook style info on places, sights and things to do in Chitwan, it's a good general guide, and is a good intro to Chitwan. It's not a souvenir or coffee table book - buy that later when you know what you liked in Chitwan. At 250 Rs it is definitely not a rip-off.
Favorite thing: Chitwan is famous for its tigers. I did not see any. But there are sooo many wild animals! Monkeys and antilopes are plenty. But I also saw a lot of rhinos and a black bear and crokodiles....