You statement "when below 20 F" I read that as when temps are 20 degrees F not minus 20F. IF minus 20F, I would expect the oil to need a bit of warming to operate but not be frozen even at that temp. I recently moved my
B26 from shed to shop when it was 20F with no warming at all, just cranked it at idle and raised the FEL, backed it up and pulled it into my shop and closed the door. NO warm up, other than maybe 10 seconds and it all worked. I didnt rev up the engine or anything just a slow roll out and in but no jerky movement or otherwise issues with oil temp.
Your tractor surely has some issues with the oil for it to not work, freeze up etc. You need to heat it up hot with your dipstick heater or other heating method and get the oil to circulate in the tractors system. Once the tractor hydraulic system is working, work all the hydraulics for at least 30 minutes or until the system is up to normal operating temp. This may take a while if outdoors and very cold, then drain the oil. I would unscrew the filter and drain it,to remove all the old oil, then reinstall it (no use to put on a $30 filter to flush with)then add about 1.5 to 2 gallons or about 50% of your tank capacity, of hot oil,(heat it up on a burner or deep fryer to about 180F) and pour it into the reservoir to circulate, work all the hydraulics to flush out the old oil , then drain this oil, NOW replace filter and fill with fresh oil of your choice and you should be good to go.
If you are getting water into your hydraulic system, you need to look for what might be loose and allowing water inside.