ammo.crafter, I don't have any experience with the .444, but I think it would be fine with one of the stouter bullets (Partition HD or A-Frame) or a cast bullet.
That said, many moose have been shot with a 30-30 at close range. I have a 336 Marlin that shot four (not by my hand, but my dads).
However, I would not use anything less than .270 cal (personally nothing less than .30 cal). A 30-06, 308 etc. would be fine at any range. You could use a 300 WM, 338 WM, etc., but you don't need it. In moose habitat, you will be hard pressed finding a shot over 100 yards. The only long shot would be a shot over a marsh or fenn (don't shot it in the marsh, not fun!).
The trick I think is to have a rifle that is handy in the bush and that you can get a shot off quickly. Your .444 should fit the bill nicely. I moose hunted once with my 300 WM A-Bolt with a 26" barrel and it snagged on everything.