A 13' Scamp or Casita would work. In real world use the 15's and 16's tend to be too heavy on the hitch; your Subaru will only take 200 lb hitch weight. Other than that, the 16's don't pull much harder than the 13's so if you really could keep the hitch weight down and if you kept to 55 mph or less, you'd probably get by ok with occasional towing of a 16. Of the three, Scamp is lightest on the hitch.
Along the same vein, you could also consider the Weiscraft Ponderosa or Little Joe. These have even less frontal area than the previously mentioned brands, because the body is only 5' wide. They are still built, I believe, in Colorado.
Or you could look at pop up trailers. The A-frame trailers made by Aliner and Chalet would keep you in hard-sides (no canvas) and only take a minute or less to set up. But again you must choose a model with a low hitch weight. The ones made by Forest River and Jayco are all too heavy on the hitch, I think.
There are people who tow with Subarus, but heat is the enemy of longevity, so extra transmission and/or engine cooling is good insurance against premature breakdown.
Yes, a good welding shop might be able to fabricate a heavier hitch for your Subaru, allowing more weight. But it is costly (I got a price a couple years ago from Can-Am of $1900 to modify a VW Jetta) and your drive train's performance in the mountains will already be marginal, so why push it.
P.S.-- You will never get one single, definitive answer on your question. Everyone has had a different set of experiences and has formed different opinions. I once towed a 13' egg from Michigan to Colorado and back, with a '84 Dodge Omni 2.2L 4 cylinder and 5 speed stick shift (1000 lb tow rating). No trailer brakes. We had a nice trip, without incident. Can it be done? YES. Would I advise doing it again today? NO. ;) I was overloaded. But in the end, you will believe what you want to believe and will make up your own mind.