Welcome to CT!
The roads can be hit or miss. If you are on a state cleared rd (route 6, etc) it shouldn't be too bad, as the state workers love to put in extra hours plowing nothing. You can check out CT dog parks here http://www.dogparkusa.com/connecticut
I've only been to the Norwich one and my aussie/border collie LOVES it.
As for cool things to do....yeah ummm...Eastern CT can be pretty quiet...there are a few cool places like the Willimantic Brew Company and the casinos...shopping and dining in Manchester. But other than that, I can't think of anything.
Have a great time!