The Tecumseh 4 stroke engine on my (old) Ariens snow blower has
progressively required more choke to keep running.

Everybody might be right. Too much air OR not enough gas.
If the carb is loose, suspect the air problem, a relatively easy fix,
although getting a wrench on those bolts can be a knuckle buster. Don't
round the corners off the bolts, eh?
If the carb is tight, then suspect dirty jet(s), which can only be
fixed usually by tearing down the carb and blowing out the orifices
with comperessed air. If you don't feel up to that, you could bring the
carb in to a small engines tech. And yeah, it will need a rebuild kit
to be fixed right, although sometimes a good cleaning will suffice.
Drain the fuel out of your carb somehow every year before putting the
thing away. That goes double for 2-stroke engines. I start them up,
drain the tank somehow, then run them till they quit, choke and start
again til they won't start no more. This prevents varnish from
evaporating gas from clogging up those jets.

JohnK