For this time period and with this level of specificity, we're going to have to rely on upstreaming later periods, which is particularly problematic in this case - but we'll get to those problems in a moment. First, let's talk about the similarities. I'll be focusing on the Haudenosaunee (Iroquois) here, since the majority of what's now New York would be their territory. We could also discuss the Mahican and the Munsee, but I don't have much relevant information on them at the moment.

By 1315, maize-based agriculture was well established in the region, and beans would also have been recently added, so we're dealing with the same agricultural suite that was present in the colonial era. In the colonial era, this agricultural system provided the vast majority of society's food needs, which was supplemented periodically by other economic activities. Because of this, hunting - setting aside the occasional opportunistic kill here and there - was highly seasonal.

The hunting season began in earnest in fall, after the harvest had been completed, generally speaking this would be sometime in October. A hunting expedition consisted of a small group of men along with a few women (typically the hunters' wives, but not always - his wife might have other business to attend to in the community so she could appoint another woman from her clan to take her place). Once the hunting party left, they might occasionally send one or two of their party back home to deliver a load of meat before heading back out to rejoin the others. If the animal was killed within a day's journey of home, it was loaded onto a sledge and hauled back without processing. Otherwise, it was field dressed and cured by the fire, before being packed away into bark containers. Generally only the best parts of the meat and the hide were preserved this way, and one of these containers could allow a person to carry the product of a dozen deer. Aside from the occasional delivery, the hunting parties would stay out until they had to return for the Midwinter Ceremony, a nine-day celebration that occurs five days after the new moon at the end of January / beginning of February. This marks the end of the major hunting season. Crafting became the dominant winter activity after this - making tools, weapons, ornaments, etc., things people could do indoors with materials they had stored away throughout the rest of the year. There were, of course, winter spots to play, too, so you wouldn't be spending the whole of February and early March locked inside your longhouse.

Once spring came around, women started planting and men started fishing. There'd be the occasional hunt here too, especially if the forest needed burned anyhow. Unlike the fall-winter hunts, these were community-based drives, in which dozens - sometimes even a hundred or more - deer from a small area might be killed at once. While the fall-winter hunt was selective (only bucks could be killed then; does couldn't be hunted), the spring communal hunt wasn't picky. Summer was the season for councils, festivals, sports, and warfare. Early fall brings the harvest, which in turn brings us back to the fall-winter hunt.

This seasonal pattern is, of course, generalized and there were deviations from it now and then. During the 1649 invasion of Wendake, which kicked off the Beaver Wars, the Haudenosaunee exploited this cycle, launching their attack in winter rather than summer to gain the element of surprise.

As for how far the hunting party would travel, that's where upstreaming starts to fall apart on us. The information we have concerning Iroquoian hunting largely comes from after 1700, by which point they had greatly extended the reach of their hunting parties. Could the Seneca have gone into Ohio back then? They would have quickly run into the Erie and the Monongahela had they done so. Could the Cayuga have gone all the way down the Susquehanna to the Potomac? The Susquehannock and the Piscataway might have had something to say about that (especially the Piscataway, whose oral history would indicate that they were their political peak in the 14th Century, during the time of the tayac Uttapoingassinem I). Could the Onondaga have gone north into Canada - or would Hochelaga have kept them out? The Mohawk might have had a relatively easy time of hunting in the Adirondack Mountains and around Lake Champlain, as they did historically, since the area wasn't heavily populated (though the lake was also used for hunting by the Abenaki to the east).

Without the peculiar economic conditions of the colonial era, however, our Iroquoian hunters of 1315 probably wouldn't have had to travel that far anyhow. Assuming that the Haudenosaunee had a similar population as they did in the colonial era (around 20,000), they'd need about 15,000 square miles of hunting territory in order to keep everyone clothed in deerskins sustainably. This is just a rough estimate based on figures taken from the Wendat (Huron), which were estimated to need about 13,000 square miles of hunting territory for the same. The Wendat seem to have gotten by with only about 10,000 square miles prior to the 1649 invasion, so the figures are either overly pessimistic about what was really necessary (the study essentially assumes that every adult is wearing a full deerskin outfit all the time, which wouldn't be true, especially during the summer) or the Wendat made up their deficient by trading with Algonquin hunters to the north. Either way, that rough estimate of 15,000 square miles is less than a third of modern New York State, so they might to stay relatively close to home to accomplish their hunting goals at the time.

You might also be interested in How much do we know about how the Iroquois would have hunted?, where I discuss the techniques of hunting more.