I am no pro installer and I have installed both projects this far at this house in Arizona summer.
Mortar is a water based product that needs to stay unfrozen to cure. I am pretty sure your garage would be fine to start working, especially if you start the tiling at the door, which will require the door be open obviously, so doing that mid-day it should be at least in the high 50's up their. Once you get the area under the doors done, you could work comfortably indoors, augmenting heat with a fan-powered garage heater. I am sure your closed garage doesn't get below freezing in October so any tiles set should set up just fine before peak cold. Same with grouting. You can grout under the doors and have them closed within an hour. If your garage faces east, it should warm up with morning sun, same with west-facing garages in the afternoon.
The only hassle is the use of a tile saw but, you can lay the main body of the tiles and then cut the edges after the main body is laid. If you have a pattern, like herringbone, that will require a bunch of split tiles to straddle an expansion joint, you could pre-saw a bunch of those and then go to town, using the saw at the very end. You could put a tarp down to catch and mist from your wet saw. You can always hose your whole tile job down before grouting so, if you get some over spray on it, its not a big deal.
Sure... I'd go for it! Take lots of pictures and start a thread here!
Ray