I really like the idea of the pole axe weapon, but I’m having a hard time deciding what unit to give it to, I want it to be a tankier unit that I will eventually give distant counter, like Frederick, Christmas Chrom, summer Xander,

Sheena/Camilla could work too

frederick and xander don't seem like good distant counter users and chrom has high enough attack to kill most horses anyway. camilla, sheena, hawkeye or titania are probably the best options

Honestly i had the same problem i wanted to give it to a axe infantry unit but after looking through the list of greens I decided to just wait til IS introduce more to the game.