Regular tire chains won't help you much on a side hill, go for the double diamonds. I have tried all kinds of chains on steep slopes, double diamonds work the best. Labonville is a good place to get them.
As for a machine on a side slope, that is one of my specialties. I do erosion control, road building and excavation on a lot of terrain similar to VT. A small excavator (3-8 ton) works great in the summer months, don't even try on snow/ice. Ledges are problematic, but if you plan your moves you'll be ok. Tractors are ok in some situations, but not for steep sideslopes. As soon as you try to pull cross hill you're going to slide. Plan your roads for up and down, and cut the side hill roads into the slope so they are level. This alos helps with erosion issues. Dozers have some of the same issues. You'll get more done with an excavator, but a dozer will get by.
Good luck, be careful. Be sure to load the tires and buy wheel weights. Load light and go often.