Well, this is a very debatable subject, as to when is the best time to hunt. I have hunted Moose during all three of their "hunting cycle":
The early season moose hunt is done mostly over water, as bulls are feeding on aquatic plants at this time. Also hunting parts of the high country will produce good bulls.
It is probably the hardest time to hunt these mammoth creatures, as the foligae is still quite thick and they will be hard to find. Although while the antlers are in velvet, they are soft and the bulls will want to inhabit less dense bush until the antlers harden.
The moose-rut hunts run traditionally between. During this time moose respond to calling and are usually very active.
I find this time the best for the trophy hunter. Bulls are on the move gathering cows for their harem and very susceptible
to the call (either cow calling or the bull grunt). This allows the hunter to look over several bulls before having to decide on which one to take.
The late season hunt is excellent as well, because there is usually snow on the ground, which makes it easier to locate the moose. Moose are generally feeding on willows in logging areas, around lakes, as well as in old burns. Seeing where Moose are the most active is also much easier during this timeframe. A wounded animal is much easier to track in fresh snow.
This 'season' is not for the faint-at-heart, as the weather will not be the hunter's friend and bone-chilling cold is more the norm than not. Those huge black bodies certainly stand out, especially when there is no vegetation (except conifer trees) to hide in and the drastic contrast makes them stand out against the white snow. Probably the easiest time to recover the Moose as it can be dragged easily on top of the snow.
BLUE COLLAR ADVENTURES REPRESENTS EXCELLENT OUTFITTERS
EASTERN CANADIAN MOOSE - Newfoundland (can be combined with Woodland Caribou)
CANADIAN MOOSE - British Columbia, Alberta, Manitoba and Ontario
ALASKAN-YUKON MOOSE - Alaska, The Yukon and The Northwest Territories