Upright piano in front of a drafty window?

I want to get a used upright piano, and it seems like the best spot
for it would be in front of our living room window in our apartment.
We live in Chicago, and get drafty winter winds! Window is a bit
drafty, but not too bad. Would the draft in the winter be bad for the
piano, if the draft isn't THAT bad, but nonetheless can be felt?

We have an awning outside and curtains inside, so I don't think the
sun would be a problem (like I saw in another question in this forum).