Once the OP got the tractor back upright, letting it sit for a while was a good idea.
And if the engine started and ran reasonably for any length of time, even three seconds, that means the engine is probably in good working order still. If the engine was Hydro locked or something else, it...
This is what I do except I always plow in reverse so I don't pack the snow down with the tractor before plowing it.
If driveway is frozen: drive in reverse with blade facing backward (so indented part of blade is closer to the tractor)
If driveway is not frozen: drive in reverse with blade...