My guess is the battery is just fine. A cold battery makes things worse so if it's in a building with holes in it where the wind can get in or maybe with a dirt floor, that makes thing colder than in a shop attached to the house. Things turn pretty slow at 2 degrees and windy.
Next summer, have a dealer install a block heater that will heat the coolant and you will be all set for next year. Don't try to put it in yourself unless you have done it before since lots can go wrong.
I know what you mean about the block heater.. I put an OEM in last summer, I tapped the plug on one side gently and couldn't get the plug out, I didn't want to tap the punch any harder, I called my brother (he is a diesel mechanic) he told me to take the punch and warp one edge and grab the plug with a pair of needle nose, I got it out no problems, I use it all winter, the tractor is as cold blooded as it gets so the block heater and tender is going to be needed in the winter months I guess..