I'll touch on a few things here.
For the OP, I think it is a good idea. Take weather and bad roads into consideration, but I also find that spots that hold birds later in the year are likely to have them all the time. I know some smaller parcels that I hunt early in the season aren't worth the effort later in the year as they just don't provide the thermal habitat. If it were me, I'd hunt some spots and discover where they are roosting in the late season.
I opposed the season extension for the same reasons mentioned here. However, if pheasant hunting is legal, I have a hard time seeing Sage and I sitting at home on a weekend afternoon. With that said, I anticipate hunting cautiously as I do believe that the added stress of being pushed from cover in tough January weather has the potential to be detrimental to hens, which are already smaller and weaker than roosters. At the same time, it isn't unheard of to get some warm, 20 degree days that time of year, plus, there are plenty of other factors that could go into stressing the birds. All that to say, if the high is 20 on Sunday and isn't going to be brutally cold for a few days, I'll try it out. If it's 5 degrees, windy and snowing with a lengthy cold snap in sight, I'll probably give them a pass.