In the UK and Europe all washers and dishwashers are now designed to work off a cold water input only, heating the water internally as required. Older washing machines used hot and cold inputs, so for a newer washer or for a dishwasher just the cold feed gets used.
The cold water feed is important to dishwashers as that's what enables the condenser drying function to work. Smaller, portable, table-top ("ultra-compact") dishwashers are very cut-down in features so typically lack an in-built water heater and must rely on a hot water feed instead, but the water they draw is usually just the cold "dead-leg" which precedes a proper hot water flow. That means they either clean relatively poorly, or need to waste water as you run the feed hose into a sink until hot and then connect it to the dishwasher. Ultra-compact machines typically lack any form of drying, so the lack of a cold water feed isn't an issue.
Modern washing machines are usually cold feed only for similar reasons, if a hot feed is connected then it only tends to draw the cold dead leg and so still has to heat the water internally but will also have drawn hot water from the supply tank into the supply plumbing to replace the dead leg so wastes energy. Keeping the machine to cold feed only ensures that the machine costs a bit less to manufacture, has fewer parts to go wrong, and means that only the water required for the wash is heated and only to the temperature required. Given that there's a growing move towards cold-water washes only, or for tepid washes at 30C in the UK/Europe where we use far lower enzyme content in our washing detergents, cold feed machines use less energy than those with an additional hot supply. Once again, it's only super-basic ultra-compact washing machines which may require a hot water feed.
The dishwasher has only one water intake, and that's for hot water, so you would have to do some plumbing to hook up a washer else you're using hot water on everything. Washers generally need an open, vented outlet in order to drain properly. Start using your dishwasher -- dishwashers actually save on water and electrical usage.
Take a look at the little Panda washers -- they come in two sizes, and most people could find someplace to tuck one. I got the larger 10lb model as a temporary measure whilst redoing the bathroom/laundry area, and I like it so much it has become my permanent machine. Cleans remarkably well. Watch Alaska Granny's video for the basics. My larger one has water inlet on the spin dryer side so you can rinse using that, whereas I don't believe the smaller model has that feature. The spin dryer works so well that clothes come out almost wrinkle-free and dry in no time on a drying rack, or small portable dryer.
Yes. It will swap with no problems at all.
