In my opinion Feb. - Mar. is prime time for riding the Southern Tier route. You will have frost quite a few nights in the western half, but most likely will have pleasantly cool daytime temperatures most of the way. You will definitely see lots of open country in the West on that route. I found the scenery a little monotonous most of the way, but enjoyed the route none the less.
The eastern half is likely to be cool and mostly fairly pleasant with a chance for some moderately cold weather.
Higher elevations can have snow at that time. There aren't many passes on the ST, but I saw just a little snow when I did the ST at that time of year going W-E. Of course there could be more. Your Grand Canyon route is probably higher and high more of the time, so it would probably be more likely to have cold and snow. I'd think the chance of it being truly cold or very snowy are fairly likely around the Grand Canyon in Feb. and early Mar.