Craig, Carey and Winston covered it well. Your Yanmar might be an early one with a TS button on the dash instead of the twist-left ignition switch. Same idea.
My coldest-weather starting procedure:
*Throttle zero, use the compression release, crank with no compression until the oil light goes out.
*use Thermostart for about 6 seconds. (Many Yanmars have the Thermostart wired to both the TS and also the Start key positions, so this along with the no-compression cranking adds up to about 15 seconds of TS.)
*set throttle at Full Throttle. Don't ask me why, that's what Yanmar put in all their manuals.
*Use the compression release, start cranking. When the engine is cranking at full rpm drop the compression release. With the flywheel inertia assisting the starter, it should fire right off.
* Pull the throttle down to mid range immediately. Yanmar says warm up at 1500 rpm for 5 minutes before any load. (I wait 3~4 minutes then drive gently for a few more).
*If it started with a fog of white unburned fuel vapor then next time use shorter time on the Thermostart. If you got a huge cloud and it didn't start, spin with compression released and throttle zero to clean it out then try again with less TS.
A couple more points:
*The later 3-cylinder Yanmars start easier in cold weather.
*15W40 Diesel engine oil is the current recommendation for old Yanmars. I might try winter rated synthetic for real cold weather use.
*A battery has something like half the cranking power at zero degrees compared to warm. I have left a trickle charger on overnight to help warm the battery. A 2/10/50 amp charger set on the start-assist mode works great too.
Carey - the weather here (North of San Francisco) is spooky warm. Sunny, mid to high 60's (record highs) and predicted to go on indefinitely. It feels like May. Winter here should be highs in the mid 40's and with most of the year's rain falling in January and February.