Could I use a pressure washer on a house with a well pump? Should I be concerned about the pump running for a long period of time i.e. 4 hours? half a day while we wash the outside of the house?
Most consumer-grade pressure washers require the input water to be at least in the low range of typical household pressure from a municipal water supply. It also needs to be continuous; if a well can't keep up with the demand, you'll destroy the pressure washer.
But, there's an option: operate from a tank of water with a pressure washer that can operate with a siphon feed.
Even small gas pressure washers typically use 2.5 - 3.5 gpm, so 4 hours of run time would require on the order of a 600 - 900 gallon or larger tank. But a gas pressure washer can clean a large area quickly, so you may not need 4 hours of run time. Electric washers use half of that.
You prefill the tank at a convenient time. You can also fill it with captured rain water, like from your downspouts, that you filter REALLY well.
While most consumer pressure washers can't operate from a siphon, there are a few that can. For example the high-end Karcher machines can, and they sell a siphon adapter kit for them.
If you can rely on your well for continuous volume at around 2 gpm, you could feed a siphon-capable electric washer without needing a tank or worrying about run time.