Well, I am going to add my 2 cents and probably create a firestorm.
Conventional wisdom has always been that a standard transmission was more suited than a for hills and pulling a load. However, the hydrostatic drive transmissions and automatic transmissions in pick-ups have come a long way and holding up very well. I have a 3 speed hydrostatic drive on a little massey ferguson and it may be the best thing on the tractor, other parts and system on the tractor have failed miserably. As for a transmission, I think it is a coin toss and personal preference.
What about a cab? A cab is really nice in the winter pushing snow when the temperature is 20 degrees or less. However, you mentioned mowing mountain trails. What about tree limb over hang on your trails? Will a cab clear any branches.
Farm? You mentioned a farm. How many acres a involved? Is it mostly cattle and hay? Are you growing and selling fresh produce? Are you raising field crops? I would suggest the minimum requirements. 4 wheel drive, a front end loader (possible with fork depennding on what your plans) fluid in rear tires for added rear weight and traction and a set of chains for the rears. Generally snow does not hinder those little four wheel drives, but packed snow and especially ice can hinder you. A set is chains on the back should be enough to grip and get you moving. As for tires, I would go with an ag tread verses industrial or turf tires. I think ag tires provide the best grip.
As for the size of tractor? I generally like a little more tractor than necessary. No power issues and easier on the tractor. Things just seem to go better. If your growing produce, I'd recommend 40-45 hp. Give you plenty of tractor for a brush hog an bigger tiller. Should also handle a 2 bottom plow and small disc.
If it's cattle and hay, I would bump up to 50-60 hp. One again somebody going to claim they pulled a baler with a 25 hp tractor. People will say you only need 35-40 hp to pull a baler. I pull my baler with 70-80 hp tractor. I got plenty of tractor, tractor nearly plays with that baler, not hard on tractor and things seem to go better. If you have a 60 hp tractor, you can set round bale with 3 pt bale spear. Don't know if modern 60 hp tractor/loader will set round bales. It should, the old ones did it. I think the old ones were more beefy than some of this neew stuff. A 60 hp tractor should pull a 3-16 plow and 10-12 ft disc.
Here is were a 300-500 hp tractor comes into play and is relevant. I live in the heart of the farm belt. You got guys turning 1000 (s) of acres. Nearly everybody has John Deere or case-ih. Some of these tractor brands I didn't even know existed until I found this sight. I know guys and I'm one of them who bought light utility tractors and they did not stand up. The work on 10 acres close to town. I won't mention brand names, but pretty much everything around here is John Deere and case-ih. The guys that have the big stuff also need utility tractors and light utility tractors. They are sticking with John Deere or case-ih and they are holding up pretty well. John Deere and case-ih have a vast parts network and dealers are all over the place. However I have heard that John Deere and case-ih light tractors are not near the quality of the big ag tractors. Brand is up to you and everyone has their reason for the brand they like. But, I would encourage you to take a good look at John Deere and case-ih.
