Pressure washer

Nope. need to make the droplets that freezes to become snow. Otherwise you just have really cold water.

what if u used warm water

it will just turn into ice. So, no.

You can do it. It won't be cheap or easy though. If you can't afford an aircompressor you won't be able to afford the following..

Our resort uses airless guns for touch ups on some of our hills now. The key thing is the bacteria in the water to help the nuculation. By pumping water out of a pond or stream the bacteria is there as city water will have cholorine etc to remove those elements. The water has to be super cold at just above freezing and you have to combine snowmaking chemicals such as snowmax to it. Snowmax runs at about 100$ per bag and a bag will last you about 2 nights of snowmaking based on 1 power washer.

The other downside is the gun will have to be about 15 feet in the air, and can only be run in light winds, - 10 or below and low humidity. Impossible no, pain in the ass. Yes.

you would be better off building a cheap gun and getting a compressor, it would not cost you much more and it work a lot better

Its been tried.  Unless you have a really really high nozzle position and really cold temperatures, you'll never get crystallization.  You can actually make a working gun without a pump (pressure washer is a pump), but you can't do it without a compressor