Not likely, if the starting engine is in good condition, hot spark and plenty of fuel, that's where they shine, you get that starting engine, (most call it a pony motor) running, more than likely the diesel will fire. You might have to spin the diesel awhile before you turn the compression on. I have the same starting engine in my D7's and I recall one winter evening, after a pick up hockey game on our pond, one of my friends, thought his brand new chevy 4x4 would make it through deep snow on a side hill, along the pond, had to be different, LOL, not park on the flat, where it was cleared, well I had to put him on the ice to get it turned in a good direction and a running start out, but it was deep snow, cold, in the teens. I had a little work to do on the starting engine, but I got it fired and just let the diesel spin, a good while she came to life, and down I went to get a line on him, and tow it out, late evening, I was pushing deep snow in the dark,(it was fun too!)
The one thing that does amaze me, is that the D7 is basically the same engine, but 2 less cylinders and the starting engine will lug right down in the cold, have to give it time before you raise the compression lever, the D13000 6 cylinder has to be about all one of these can take, probably needs to spin even longer, and be in good tune to deal with it.
If thats an 8R series, good chance it wore OD Green under that yellow at one time, not as common as the D7's in WWII but there were quite a few bought under government contracts, tracks seem to be in nice shape from what I can see, and still a very handy tractor around any farm.
Don't mind me, its just you posted a real nice example of one of my favorite old tractors !