Up side to late season;
It's normally cold, so the dogs work harder vs. early season/warmer temps.
There's normally snow cover so tracking is possible.
Birds are bunched up. Once you find them your into birds--a lot of them

.
You'll see more birds in the late season than any other time of year.
Very few hunters/pressure.
Lodging is cheaper in the late season.
Birds stay frozen in the cooler so no ice necessary.
The down side to late season;
Hen to rooster (flush) ratios can be low. (With that said, a few years back I spent a week hunting the late season. For some reason the roosters wouldn't come into roost until after dark

.
That week was a hunting trip with nothing but hundreds of hen flushes through-out each day. The week after that, the roosters moved back to normal roosting habitats/patterns and hunters were back to dropping roosters.)
Birds can be jumpy. In some fields, you'll get a few yards within the field and the birds are already flushing at the other end. Still a nice sight to see!
Some of the roads may be snow covered and very difficult to travel on in late season. Unfortunately a few of those roads are the only way into some good public lands so it may be a case of park the truck and start walking to the site. No big deal.
Most of your hunting will be in thick cattails, though they do move within grassy areas too--weather and snow cover effect this greatly.
P.S.--if I had my choice as to when to hunt wild pheasants in SD it would be (hands down) December/late season. That's my personal preference

.
Hope that helps!
Nick