Unfortunately, this is the expected behavior. When you first start your car on a cold day, the transmission fluid is cold. This makes shifting more difficult (requires more pressure) and can cause undue wear and tear on your transmission.
Ideally, you'll want to warm up your car before you start out. 1-2 minutes should be enough during the Fall in most US climates; it can take as much as 5-10 minutes for transmission fluid to reach ideal operating temperature in more extreme winter climates.
Be sure, also, that you are changing your transmission fluid every 30k miles or 2 years, whichever comes first. It's far, far cheaper than replacing (or repairing) your transmission.
If there is not enough transmission fluid in your car's system then this could cause your transmission to not go into gear until the car is warmed up. You could also have a professional take a look at your vehicle for a minimal amount or free estimate.