Miroslav - your idea of building a "tent" over the cab is actually something that I should have tried by now and I absolutely will. I'd imagine you;d need some pretty heavy comforters to get any moderately broadband reduction around it....
As in the pictures....I use two thick comforters, the second, top one is pretty heavy.
Of course...they don't provide soundproofing, though there is a good drop in volume in the room, which allows for more amp volume than without....and the main effect is that it makes for a very dry signal going into the mic....which I sometimes want for rhythm guitars.
I've also used the tent around my Hammond extension speaker cab, for that same
reason, but also to prevent any outside noises from entering the mic.
I first saw this "trick" while working for awhile at this
studio back in the mid '90s. It was used on the kick drum.
The engineer took a second kick drum shell (no heads) that was then placed in front of the actual kick, almost touching, then the mic went out in front of that shell, right at lip....and then, about 3 huge blankets were paced over that entire rig...covering most of the actual kick drum, the second shell and the mic...turning it into this huge blob.

The kick was really dead, but with huge
THUMP. That second shell funneled the sound right at the mic...like a tunnel.
I never personally tried that when recording a drum kit....but I figured the same tent principle could be used for guitar amps/cabs...and it works quite well...though it's extra work to set up. If the amp is
a combo, with the controls inside the tent, it takes more time to dial the amp in, and you have to keep reaching in under the blankets to adjust, and then cover up to check, then maybe in again to move the mic, and again chec...all the time trying not to disturb the whole tent setup too much.
As I mentioned....I don't do it as much as I use to initially, because after a lot of recording I saw that
my studio was not very "live" or that it was adding too much room sound to
tracks....so the amount of ambiance in most cases is just right, a touch of woodsy room sound, but occasionally I still want a really dry/dead track so that I can FX it later, so then I break out the comforters and I build a tent....light a campfire, grill some burgers....
