I haven't cycled there, but I did spend 7 weeks up in the far northern reaches one summer. I suspect that cycling might be more appealing then horseback riding (they BITE), but it would be a significant challenge to travel very far by bike, at least in the north! You would need a method for crossing rivers, as the dirt roads go straight through them, and there is little to no infrastructure most places. And I hope you like vodka, as anyone who meets you will probably offer some!