You can take your battery/s in for testing at an auto shop. They can tell you if there is a bad cell or working well. I have never heard of pushing the key in, to warm up the glow plugs. What kind of tractor do you have? Is it new? The older diesel tractors here all need the key turned left, I count to 15, then turn key fully right to start the motor.
Anytime you can keep tractor sheltered, garaged, in the barn, is better than leaving it exposed to the wind outside.
If you do plug in the block heater, I only leave it heating 20 to 30 minutes.Heaters are quite effective, do not need to be left on all night or for several hours. Shorter warming time also reduces chances of fire. Locally, we have a couple barn fires every winter from “warming up the tractor” issues, like being plugged in all night, leaving chargers on for hours, hot light bulbs under the hood. Long times with heater plugged in will burn your oil, reducing its effectiveness, needs changing much sooner. I can put out hay, turn out horses, tractor should be warm, ready to go by then. Even in very cold temps.
Unless tractor has been difficult to start recently, you have probably nothing to worry about. If you do go looking for a sled, the black, squarish ones in sporting goods stores are very tough, hold a couple bales, slippery on snow or dirt, mud. Heavy plastic, a bit more expensive than kids sleds, but last for years.