The Toolcat 5600 has a 48 HP Kubota engine. Using the 3% per 1000 feet rule of thumb for HP loss versus your 8000' altitude (discussed a lot on TBN), that ends up being effectively 36.5 HP (48 * (1 - (.03 * 8))).
The Toolcat 5600 Turbo has a 58 HP Kubota turbocharged engine. Turbo motors loose very little HP versus altitude, so this means you actually get most of that 56 HP.
Since by definition you will be pushing any snow removal implement ahead of the Toolcat, its tires will not have to dig through deep snow. If you look at the Bobcat website, you can find a lot of information and articles on using Bobcat equipment, and specifically the Toolcat, for snow removal.
Also, the Toolcat 5600 Turbo weighs 4820 lbs with no attachments. In the case of moving snow, weight is your ally. Still, I'd have a set of 4 chains around. At least the Toolcat's tires are relatively small so the chains will be fairly inexpensive. Note that the down side to using chains is that if you run them on paved or concrete driveways, they can mark up the surface, especially if you spin the tires.
BTW, with your annual 180" (or 15 FEET!) of snow fall, I'm thinking you'll really want to use the high flow (I believe the 5600 Turbo Toolcat includes the high flow option) snow blower attachment so you don't have to worry about where to pile up all that snow for the whole winter. And at 8000' in Colorado, that snow will be around all winter.