By RAW, it depends on what you are crafting; Yes, for some things.
As per the “Tool Proficiencies” section in Xanathar’s Guide to Everything (starting on p. 78), with the correct tools many things can be crafted during rest periods. Each of these are specifically mentioned in RAW.
You can make basic alchemical materials like acid, alchemist’s fire, antitoxin, or soap during a long rest.
Ditto a meal or a forged document takes a short rest.
Repairing metalwork, so smithing, can be done at 10 HP per hour but stipulates you need to have a hot enough flame to soften the metal, which in the real world means you need a forge wagon to do while afield, but here might be accomplished with magic.
Clothing can be created during a long rest, or repaired during a short one.
Arrows can be crafted during a short or long rest with woodcarver’s tools.
Crafting a map is directly stated to something that can be done while traveling with cartographer’s tools.
Painting and drawing is stated to be doable during rest periods.
Crafting also falls under the downtime activity rules (Xanathar’s, p. 128), 50 gp value per 40 hrs of work, including some of the above as examples, implying some overlap and allowing us to compare time and progress.
The implication is clear anything you might reasonably be able to do with the tools on hand, you can do it, but other things are nigh impossible because the equipment or material is not portable. Notably masonry, glassblowing, and leatherworking lack any mention of rest activities which makes sense since these each require significant time and non-portable equipment or are themselves not portable (note in the real world harvesting a hide is very different from turning it into leather). Even smithing only allows for repairs with a big qualifier attached.
To use arrows as an example (XGE, “Woodcarver’s Tools”, p. 85), you can create 20 arrows during a long rest or 5 during a short rest, using downtime crafting 20 arrows takes about an hour (1 gp, 0.8 hours), so there is definitely an implication that crafting on the go takes a lot longer, about 4 times as long when it is possible at all. This makes sense since you would not be able to devote your full time and effort into it.
Yet something like an 50 gp antitoxin also takes a long rest (XGE, “Alchemical Crafting”, p. 79), presumably because the cost reflects material cost not labor, which makes sense given the cost of raw materials given (50 gp per pound).
So it is up to the GM whether it is possible (do you have the necessary tools and raw material). How much you get done is not well-defined, but a good rule of thumb might be 1 gp worth of labor per long rest. Keep in mind that D&D is not supposed to be a high-fidelity life simulator; just because it doesn’t talk about it does not mean you can’t do it. Nowhere does it tell you you can bathe or how to construct a campfire either, yet few would argue you can’t do these activities.