There are a lot of trails in CT. We do have a lot of State Forest. If you are in Rhode Island there are state forests in the Eastern part of CT for riding. Let me find the names and post them later? (I just woke up) lol
Check ouy www.equinesite.com and choose RI and CT for information. Maps and groups to contact are there. Lots of green space in both states. Have fun. Check out the Pedlar for a calendar of events for the month, too. In a recent study done by the Santana foundation, RI has one of the highest number( if not THE highest) of horses per square mile in the country.
And if you are looking for a little getaway, try Grace Note Farm in NW RI. Bring your horse and enjoy the amazing meals that are prepared for you (3 per day!) We sometimes just go for 1 night so we get to ride 2 days (afternoon the first day and morning the next). It is like a mini vacation and the horses seem to really like their accomodations to. Here is the website.
For great trail riding JeanM already posted some links. I second Arcadia Management area (the midway area is AWESOME, mowed paths through fields etc..) and Goodwin as well as Natchaug state forest in Eastern CT. Pachaug is my least favorite of the bunch. The footing on the gravel roads is really hard and the wooded trails tend to be narrow and rocky. Its fine if you like to do alot of walking.
For trail rides with jumps Tyrone Farm in Pomfret, CT has a pretty varied calender including the famous Pomfret Hunter Pace. All of their pleasure rides offer the option to jump XC as well. If you have never been it is a fantastic venue and always really well run.
Aquidneck Island, Apple Knoll, Pomfret and ONBH all have fantastic jumps and hunter paces well worth the travel. Aquidneck most of the jumps are stadium jumps in a field but the scenery and footing conducive to cantering make it worthwhile. It actually goes through a vineyard with ocean views!
On the New England Arabian Trail Organization (NEATO) website http://www.orgsites.com/ct/neato/ there is a list of places to ride with directions. That's probably a pretty good source. Though, alot of these places will probably not have jumps, as they're primarily intended for people who don't want to jump over things. :-)
I recall seeing quite a few jumps in some conservation land in Dover, Mass, but that's probably a good drive from where you are, and I don't recall the name of the specific chunk of conservation land.