I think that the best way I can imagine this working with strictly acoustic instruments would be to have something other than the instruments themselves, though I'm not completely sure what it would be. This would be similar to prepared piano in some sense. My thought is that you could have something that the instruments project their sound into that would have a very resonant quality, particularly for higher frequencies, as the reverb that we hear naturally typically has more emphasis on higher frequencies. This would definitely be easier for some instruments than others. Since horns and many woodwinds have a more directional projection, it would be easier to direct their sound into something but something like a drum or strings might be harder since they tend to project sound less directionally and/or would have a more difficult time directing the sound due to size or proximity to the body, like a violin being right next to the player's face, which would require they basically have their whole head inside whatever this reverb creating device/thing is.
I'm picturing some sort of large, metallic cone, almost like an oversized mute for a horn, with some extra space or redirection to project in more than one place. With the right shape and material, I would expect that you would get a similar effect as a mute but less drastic. Ideally the device would also be able to take some of the sound and project it more directly to the listener and allow the rest of the sound to be bounced around within the device enough that it delays the sounds arrival to the listener. The direct sound would be the Dry signal and the delayed signal that would have its tone altered would be the Wet signal (if you're not familiar with those terms, you should look into reverb effects units for further understanding).
I imagine this approach would be limited in a lot of ways. You'd be very unlikely to be able to accomplish the reverb of a concert hall or anything with a long decay but could more likely accomplish the sound of a short plate reverb or small room reverb.
The only other thing that comes to mind is along the lines of what Laurence mentioned in his answer. If there were a horn that you were trying to get a reverb sort of sound on, you could try to have a second horn player playing a little behind, quieter and sustaining notes a little longer if they are staccato or followed by rests. I would also have the second horn use a mute of some sort to affect the tone similarly as I described above, where the mute would hopefully have a little more emphasis on the higher frequencies.
Ultimately, it would be very difficult to authentically simulate reverb on acoustic instruments as you're hoping. You may be able to come close with some of these suggestions but there are ultimately limitations to how effective this would be without a lot of experimentation, potentially a lot of money and a good amount of ingenuity. Developing a proper device to project sound into would likely take a lot of creativity and time experimenting and depending on what the solution is, it could be costly. If you do manage to come up with something to effectively accomplish this, I would definitely be interested in hearing how it came together.