I have a recent HVAC system and not too long ago I had to remove the blower and lube the bushings because it had frozen. This was with the AC
Now, that's its cold and we turned the heat on the blower either comes on for a bit and then quits or doesn't come on at all. I can turn the AC on and the blower works fine. Also the sq. cage moves freely. Any thoughts would be great.

Heat and A/C usually use a different winding in the motor controlled by different relays. For heat, the blower is also controlled by a limit switch. The blower doesn't come on until the limit switch warms up and closes. So the problem could be the motor itself, the relay, or the limit switch, or some of their wiring. Most often it is the relay, and on most newer systems it is on a circuit board, hard to diagnose and replace except by a very expensive new board. While you are working on the problem, you may be able to get some heat using the fan on switch at the thermostat.

Please check to see if your thermostat has batteries. Often times the batteries will be just strong enough to send a signal to the ac controls , but not strong enough for heat. I just experienced this again today. More often a battery problem will kill all controls, but not always.