Is there any reason you could not put the butter in a tray or small mini-loaf pan or whatever with individual compartments to contain it if it starts to melt? Seeing Strawman's photo of the melted butter got me wondering why would this not work? It would re-solidify when put back in the fridge before de-panning. I would think a silicone pan something like the one below would be perfect as you could easily pop the solid butter back out. Even freeze them in a bag for long term storage.
Or am I totally missing something about when the butter starts to melt and the way it would absorb smoke or taste after re-solidifying?
This baking pan is silicone, made by Wilton (it's a mini-brownie pan) and the compartments are 1.5"x1.5"x3/4" deep. It would make 24 individual "fat" pats of smoked buttery-liciousness? Of course silicone pans come in many shapes and sizes, and a mini-loaf pan would be great for a 1 pound (or so) large hunk shape. I just like the idea of the small individual portions. I would think they would absorb the smoke flavor faster due to more surface area being exposed vs the total mass of each compartment. You would probably need to soften or even melt the butter to put it in the compartments of this pan. That's why I first thought of a mini-loaf pan. Here is the link to the mini-loaf pan, says each loaf is about a cup capacity (could not get the photo only for posting):
Here is the brownie pan for individual "fat pats".
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Edit to add another thought....
Why not just take a pound or two of butter and soften or melt it into a flat baking pan/sheet. Use enough butter to get the thickness you want. Then cold smoke it (cold being relative to the ambient temp of course, but even soft room temp butter spread out into a sheet should work I would think). Then pop it in the fridge or freezer to reset and cut it into pats or whatever size you need , lift out and store. That would give even more surface area to absorb smoke flavor and likely speed up the process. In warmer weather you could nestle the butter pan in another pan filed with ice to help keep it more like room temp soft butter and not a melted slab. Best part of this idea is, we all should already have two pans this would work with.