Full support for the idea as-is, but I can easily see the dogsled becoming vehicular.
First, the sled would be modeled on the boat, allowing you to mount it, store items on it, and control where it goes. I'm fairly sure that at least in java we can't put chests on boats yet, but since we can put banners on them I suppose this functionality isn't very far away since it's basically already implemented via horses (donkeys and mules).
Next, you would take leads and attach multiple dogs (while real dogsleds can accept around a dozen, Minecrat mechanics will probably only reasonably allow for 2-4). Each dog would be forced into a specific position based on the number of leads attached, almost as if they were captured in minecarts, and would not randomly wander the way animals on leashes can. The number of dogs would represent the speed modifier (how fast you can travel).
Finally, where this gets really special is the way to control the sled. You simply ride it like a horse. When you press WASD, the sled will move and the dogs will follow. It will surely look strange when cornering, so perhaps some special momentum-based turning logic can be introduces that eliminates fast/instant 90-degree or hairpin turning like we see in player/horse/minecraft movement. This could be a fun way to introduce a drifting mechanic to allow us to slide into turns or even introduce a sled-specific form of attack (kind of like shield-bashing, just whip the sled into the enemy to knock them back.) Just for giggles, any mob attacked this way could be laid prone and given effects approximating a stun (assuming there's not already an enchant that does this specifically) and a model with track marks could be applied during that period. Grandma learned her lesson with the reindeer, but this year she got run over by a dogsled.