Will a wooden barrel with alcohol survive in soil for quarter century?

The problem would come from the fungi in the soil decomposing the wood over time. The process of lignin degradation requires aerobic conditions, so if the wood were to be sealed with wax or a charring process on the exterior then that might work to prevent breakdown. Cedar wood is resistant to this sort of degradation naturally, but only because it contains anti-microbial poisons in the wood and therefore would be unfit for alcohol storage.

We had a similar tradition in Balkans as well, we just used "Rakija" (grape moonshine) instead of Vodka. We used glass demijohns instead of oak casks when storing the spirit and burying it into the grounds. After 20 years the biggest problem was usually finding where demijohn was burried :D

In any case, I do know for a fact that we did not use wooden barrels for this tradition because water levels are really high in my area and anything made of wood would rot in couple of months and would never survive many years. If you are to dig it too shallow then temperature differences summer/winter are going to be too spread and it is going to hurt the spirit. Don't know what is the situation in your area but since you are not living in the desert, moisture is probably going to damage your barrel over time. If you ever did any construction work and found a wodden piece in the ground and if it was there for couple of years it would be all rotten and wet.

Impregnation would help but it would probably close the pores of your barrel and would prevent the barrel to "breathe" which would not allow the spirit to age properly.

I guess you want to proceed with this because of the tradition. My suggestion would be to dig a square hole in the ground (not too deep, not too shallow). Then, create a wodden casket of thick (maybe 5 cm) wooden plates and place the barrel into that casket. Make sure to remember where you burried it! This is going to be very similar to what you described, it just adds extra layer of protection to your barrel.

My suggestion would be to fill the barrel with spirit and place it in your basement. I know you are not supposed to "open" it before the wedding of your child but sampling the spirit once a year (christmas time maybe) would help you to judge the development and maybe react on time if something went wrong. Of course you would have to sustain yourself from drinking it so place it in a spot that is not easily reached.