I'd guess the L/M/H are multi-speed contacts for an HVAC-application
motor. *The voltage rating certainly makes it appear it's rated for 200V.

So shouldn't it fail if I'm using 110V? Maybe it can take the lower
voltage. I have to wonder what that does to the motor's speed and
power. Is there a way to determine what affect the contacts would
have on the speed?

I guess I can look up the model information later when I'm in front of
the motor again.

My suggestion on connections would be to ask the folks you got it from
for some guidance.

They said they pulled it from a 110V source, and that's about all they
know. They had removed it from the housing and all from an old unit,
so they hadn't read any information on it.

On the cooling, it'll probably manage a few minutes at a time w/o
cooling anyway, although the load of a mill compared to that of an HVAC
fan may be significantly higher. *What about figuring out an arrangement
to extend the shaft, perhaps?

I can try to load it with something just to see how well it does.
I'll have to mount it to something first though.

Would have to agree w/ the other responder it might not be the most
suitable choice for the job, but may get it to work. *You'll need to
gear it down quite a lot if the mill is designed for hand cranking
unless it really does have intentions for being powered otherwise the
bearings and all may not be up to the speed, either.

It's a standard thing to use some cheaves on this, at a 10:1 ratio
even. Running the mill too fast will pulverize the grain, which isn't
desired. A rough calculation is to get the mill to 150rpm. That part
isn't a big concern compared to figuring out what rpm I'll get out of
the motor in the first place, as well as what little surprises might
await me when using the motor.