In order from worst to best (Not all tires listed)

Summer tires

Normal tires

All season tires

Winter/Snow tires

Studded tires (legal in CT from Nov 15 to Apr 30)

Most people only need All Season tires, or Winter tires if they're driving in bad weather. Studded tires are absolutely better than winter tires. In CT, if you are not required to drive in bad weather, I wouldn't bother with them.

Source: Time in VT on Canadian border, having driven both with them and without them. The difference is huge, especially if you're encountering ice.

Driving slow is also very important. Even small cars are heavy and carry a lot of inertia; braking is an even bigger issue than accelerating when you're driving on snow and ice.