Any RVs that can be pulled by a SUV Jeep Liberty V6

Not sure about a trailer for you but I towed an 18' Starcarft Star stream with my Liberty and it did very well getting between 11.5 and 15.2 MPG depending on the wind and terrain. The camper weighted in at 3860# when loaded. Hope that gives you a little help

With a gasser, I would keep it small. My 21 footer is comfy with my diesel, but we are talking apples to oranges.

Yes, there are quite a few TTs 21 foot and under that a V6 Liberty could tow. Livable full time by two people, depends on your personal space requirements and ability to minimalize your lifestyle, particularly your collection of "stuff" (including changes of clothing).

Year round? If you can move to hospitable climes. In severe winter conditions? It can be done, is done, depends on expectations of comfort and covenience, willingness to burn a lot of fuel and spend some part of your life dealing with survival tasks most of us got past by the middle of the 20th century. There are people who manages to live in wildeness cabins and RV substitutes, no utiliities, no running water, in Arctic winter conditions. If they can do that, you can learn to do something slightly less extreme.

People used to winter inthe mountains with the possesions they could carry on their backs, building makeshift shelters each night, hunting and gathering their food daily. If they could do that, you could live in a TT that you can pull with your Jeep. Won't be like living in a 21st century house or apartment.

I know a few people that tow an R-Pod with a liberty but they don't live in it. It would be kind of tight but doable if you don't have much to store.
http://www.forestriverinc.com/rpod/

yea they make a few different 16-18' TTs nowadays. Ever think about a hybrid? They are pretty nice these days and in the most extreme weather days, you can fold the beds back in and make down the table to sleep.

According to Chrysler/Jeep a Linerty with the factory towing package can tow 5000# with a 60 sq ft frontal area with proper equipment. It can be 10100#, vehicle, trailer, people, and cargo rolliing down the road. There are trailers on the market that meet these criteria. Since you are likely going to be pushing the limits of the vehicle you will need to very carefully watch the weight and size of any potential purchase.

A friend tows one of the New light Colemans with a older 6 cyl Ford Escape. Think the trailer is about 14 - 15 foot with bunk beds and forward dinette.. Nice trailer and he is 6'4" and does not have to duck. Has bath, shower ect and small kitchen.

Not sure what the tow capacity is with the Liberty, but we tow a AR-One 17' with a 6 cyl GMC Envoy with no problems whatsoever. We've been on several 2-week trips and didn't fee cramped. When we go camping, we spend most of our time outdoors. I like the smaller trailers better because they're easier to tow, I can put it next to my house and, yes, can tow it with a 6 cyl vehicle that I can get 20+ MPG when not towing. That being said, if we were to take much longer trips, or had it parked on a seasonal site, I might opt for a larger unit.

This set up belongs to one of the members on this forum. I can't speak for the "comfort" of driving, or if it is a good idea. I have towed some crazy stuff over the years. (some of it I probably shouldn't have)

We tow a pop up behind my 6cyl Ford explorer. I have towed behind a 6cyl Dodge Caravan, and have towed behind a 4cyl Jeep Wrangler. The Jeep was the most challenging and I would not take it very far. The others I took well over 100 miles.

As for year round camping, A pop up could get cold. A teardrop camper will tow very well, but again for year round camping probably not the best choice.

maybe a Casita, but you'll be mighty cramped.