Taking a stove and coffee pot with you is likely no lighter than a thermos and possibly less convenient. I take a BIG thermos and have a drink whenever I want to. Let it be known that said thermos usually contains tea though. Some times I stop and set up a tarp and gather branches to make a fire. Cooking a small pot of coffee over the fire or on a small stove while roasting up chunks of kielbassa over the fire is all part of my day trip escape. I have taken cold pizza and reheated that on the fire too. That was a winner.
Honestly the best way to have coffee in the field is to have tea instead.
The fire itself may have recreational value and if you are having one any way I can see it being the way to make some coffee.. From a purely practical point of view it would for me at least be more trouble than just firing up my little alcohol burner unless I was having a fire any way. Heck, I might use the little burner even if I had a fire just to avoid sooting up the pot/cup.
I doubt it is worth it vs the thermos, but it can be done lighter than even the lightest thermos I have seen, but you need to go with a really light stove and cookware. Being a weight weenie and just for fun I looked at my backpacking gear spreadsheet for some weights. The stove, pot stand, windscreen, lighter, and cup are a setup I often have use when backpacking or bike touring. They work out quite well.
- pop can alcohol burner - 0.4 ounces
- pot stand - 0.7 ounces
- wind screen - 0.5 ounces mini bic lighter - 0.6 ounces
- Snow Peak 600 cup/pot - 2.9 ounces
- GSI drip coffee maker - 0.4 ounces
- Plastic 32 ounce cup - 1.3 ounces
That gets you down to 6.6 ounces, but you'd still need to add some alcohol. You would only need to carry an ounce or so, but the container weighs something. So lets say 2 ounces for the fuel. That gets you there with a
grand total of about 8.6 ounces including fuel.
The fire can be a fun and comforting thing, but I've never been inclined to have one at lunch time or at all on day trips. If you are having one you it saves some weight, but you still need most of the heavier items in my list. So it really only saves maybe 3 ounces depending on fuel weight.
On the other hand, if you need less than 32 ounces of coffee, there are some 15-24 ounce vacuum flasks that get to within a few ounces of the setup I listed.
In any case the thermos is just so much less fuss. You could get by without even brewing the coffee, just get the thermos filled on the way to your trip.
On the tea thing... I can't do it. If tea was the only other choice I'd just have water.