Although it may take a little more work, even when 'roughing it', you can make something hot to drink in the morning (or whenever) with very little equipment (and no electric coffee maker).
Perhaps the most familiar way to make coffee when camping is with a non-electric coffee maker. This is a device that works much like the coffee maker that you have at home, except that it doesn't plug-in.
Instead of using electricity to heat the water, it is heated over a fire. After that, the process is the same. Drip style non-electric coffee makers are available, and at least one company even makes a non-electric espresso maker.
If you don't want to haul a special appliance through the woods just to make coffee, you can pretend that you're a cowboy of the old west and make cowboy coffee. This is coffee at its most primitive. You boil water in a pan, add your coffee grounds, and let it steep. Many people then recommend adding a few drops of cold water to help the grounds settle.
Of course, this also affects the temperature of the coffee, so some just wait a few minutes longer to let the grounds settle naturally. It's helpful if the pan is set on a slight slope, so that the grounds settle more to one side. Wrapping the pan with something, or setting it in sand or soft soil, will help keep the coffee hot.
Since your goal, presumably, is to have coffee and not coffee soup, you should pour the coffee as carefully as possible so the grounds aren't disturbed. No matter how careful you are, you will probably end up with a few grounds in the bottom of your cup, so you might want to throw out the last tablespoon or so.
If you don't like coffee, tea can be made in the same way. If you're roughing it, you might have neither coffee nor tea. With a little grasp of the natural world, this isn't a problem. The ingredients for various kinds of herbal teas grow practically everywhere, and many plants have been used as coffee substitutes.
Two of the better known coffee substitutes are chicory and dandelion, which both grow as weeds around the world. In both cases, the roots are roasted, ground, and used in the same way as coffee.
The inner bark of the red birch tree makes a tea that smell and tastes like wintergreen (this is where the flavor for birch beer soda originates). Perhaps one of the most interesting, surprising, and abundant sources for herbal tea can be found above your head when hiking through an evergreen forest.
So then, whether you are 'camping' in an RV or roughing it in the woods, there's no reason why you should have to go without your morning cup of coffee, or at least some facsimile thereof.