OK, it will include work in hills, logging roads, general dirt moving, leveling, trenching, and just about everything you can imagine. Log moving, forklift work, brush clearing and moving, and some farm work. I know these are not good on frozen ground, but I will try. I am not sure what door orientation is, but I will use it year-round in hot and cold Wisconsin weather.
Thanks for asking.
So, let's break down the tasks a bit;
Dirt moving; likely a typical bucket, possible need teeth in heavy clay or rock soils, but this is a good task for a CTL. Rocky soils will wear tracks fast, and they are not cheap. If we are moving dirt very far, or in large volumes, other tools are better
Working in hills/logging trails; CTL can do this; but they are rough riding, and can high center on the belly pan. If your logging trails and/or woods are particularly wet/boggy, you might want to look for extra wide track machine. Although a CTL can often work itself out of a stuck situation, when they Do get stuck, they get very stuck
Leveling; I read this as grading; if we are talking rough grading, standard bucket does a good enough job, but if it's a bit more finished, a 6 way dozer blade or a grade controlled front leveling blade might be the best option. Take the end impliment into account when speccing the machine. A skid steer isn't a dozer, but its not far off on a smaller scale; with the right tools
Log moving and general forklift duty; for short distances they are good at this; if forklift work involves moving items a few hundred yard constantly, a compact wheel is probably better; if you are routinely moving the items in a single place (say a lumber yard), you will waller a mud hole. If you have rock in the loading area, you will wear tracks fast
Brush clearing; if this is grapple stuff, 100% a skid steer is fantastic at this, manuverable, strong, but small enough to work between large trees; hydralic mower or mulcher, these Might need a hi flow system and/or additional cooling, so keep that in mind when speccing. Visibility when moving piles is pretty limited, and it's better for pushing up piles than moving the piles once pushed up. Can be used for light root raking, but for extensive, a hoe or full sized loader is better (jd-544 type machine)
Farm work; moving bulk bags it works, although visibility sucks; demucking-manure, just size appropriately, and know manure (chicken litter is the worst, well rodent farms, I've heard rodent urine is worse...) is pretty dang corrosive, you can over come Some of this with frequent washing. Stuff like bury dead livestock/horses, TLB is better, or a mid sized hoe (Komatsu Pc-85 sized machine). If it's cleaning field side drainage ditches, TLB or small-medium hoe is better.
Trenching; although a CTL can be fitted with a ditch witch type trencher or even a front hoe, if this was a major part of the work, a hoe or a TLB is better. Skid steers to back fill well.
I am kinda split, cause it sounds like maybe a TLB, like a JD-310 might be better suited to everything but grading or "leveling"
Edit: one big down side of a proper TLB, although they all have forks available, as well as root rakes, they aren't universally interchangeable. They are also expensive. They also (atleast I've never seen it) can't have a mulcher/mower, and i can't think of a grapple being fitted. You can get a 4 in 1 bucket, which works somewhat as a grapple.
Also, portability; TLB is heavier, but can road run very well. CTL is easier to transport, but you aren't road running it anywhere