I just purchased a house and near the kitchen it has a location for the washing machine and dryer. The water heater is near by in a separate cabinet. I would like to move the washer and dryer into the garage to have more room in the house. As I was shopping for a house I noticed that many washers and dryers were near the water heater. Is their a problem with moving the washer and dryer away from the water heater?
There's no problem moving the washer and dryer in respect to your question. The column of cold in the line would be well cleared for just about any reasonable distance by the time the load is ready to wash. But it is a concern if the run is very long. For the most part you don't need hot water anyway, unless you wear a lot of whites or work as a mechanic or get greasy clothes some other way. The bigger issue is the plumbing drains. Supplying hot and cold is probably easyish. If a suitable drain and vent are not available then you have a problem.
Well, you know the problem that hot water pipes are not magic, and after a few minutes, the water in the hot water pipe will cool to room temperature. Then, when you turn on the hot, you have to wait, wait, wait while all the cool water in the pipe is pushed out by new hot water. The longer the pipe, the longer the wait. The fatter the pipe, the longer the wait squared, because of the area rule.
So. The washing machine does not know how to "run the faucet until it warms up". If you are too far from the water heater, all you'll get is that slug of tepid water that was in the long fat pipe, and warm will be tepid and hot will be warm.
The fix is to have a slop sink right next to the washer, and open up the hot on the slop-sink til it purges the pipe, then start the washer.
This is the biggest problem I can think of. Obviously, it's not a particularly big problem.
Get a washer capable of heating water internally (a regular washing machine will be ok if you're elsewhere) and hook up only cold water. Get a heat-pump electric dryer so you don't need the exhaust needed for a gas dryer, also you'll have to pull a drain line.
EDIT: Some modern US-Style hot/cold washing machine can accept cold water from both inlets, so just connect them both to the cold tap by a 'Y' and your washer should be fine (heating water internally). Just check on the instructions if this setup is allowed with your specific machine.