Will spend the night at Heathrow before returning to the US the next day. We are thinking about arriving early in the day at Heathrow and taking the train to Windsor for the afternoon. Will that be enough time to see a little of Windsor?

No train from Heathrow to Windsor; take either the No. 71 or 77 bus from the Terminal 5 bus stop. It takes about half an hour or 40 min. I believe a day ticket costs around £5 - £7 for the local bus company. http://www.firstgroup.com/ukbus/berkshire_thames/

You can see plenty of Windsor - castle, interesting old town, across the river to the playing fields of Eton - in a day. It's my preferred way to spend a day around Heathrow, far less taxing than going into the city.

You can also arrange a taxi/car service for nonstop "door to door" transportation. I still have the numbers for many Maidenhead based car/taxi companies that serve the Heathrow/Windsor route. If there are only two of you, the bus will be cheaper but the car service faster. If there are three of you (or more) the cost difference shrinks quite a bit.

But back to your original question, yes, visiting Windsor is a pleasant way to spend the afternoon.

Why not stay in Windsor overnight rather than at Heathrow?

You'd have more time in Windsor in the morning

BTW there's no train to Windsor from Heathrow - you use a VERY slow bus or a Windsor based taxi company

You could take a train to windsor but you'd have to take the Heathrow Connect (not Express) to some station on the Paddington-Reading line then switch to trains to Windsor - buses are faster, cheaper and more direct however.