I usually get about 1-2 mpg less in the winter (i.e. 23-24 instead of 24-25) - but my commute is fairly long (25 miles) - if you do a lot of short trips, I'd expect the decrease to be more severe.
New tires will usually decrease your mileage a bit (the tires are bigger and stickier at first) but again, not more than 1-2 mpg.
So all in all, I'd say it's possible depending on the circumstances...