I am not really sure this would work out. Sure, they basically have the same powers, but Elsa's job is as Queen of Arendelle. This would probably be too much of a ball and chain for Jack Frost as he has a very fun loving personality and being a King would probably be too stressful for him.
Could you redraw Jack in his colonial outfit from the beginning of ROTG? Frozen is set like the 1840s (probably when Hans Christian Anderson wrote the original fairy tale) and hoodies were not invented yet.
I dont ship them honestly, having same powers dont meant you can be lovers, best buddies more makes sense to me, also Jack are spirit while Elsa is human with flesh and blood, so its kinda make me sad to ship them.. ;_;