During the prolonged snow earlier this year I noticed that the blackbirds in my garden seemed to be finding food under the snow, (1"-2").  They would peck as normal on food I'd scattered before the snow fall, and also more generally around my rather scruffy lawn.  They weren't clearing snow from a wide area, but pecking directly down, leaving small holes.

Do they have some way of sensing food under the snow, or were they just guessing, based on where they'd found food before?

They almost certainly smell it. Many birds make their living thise way, by smelling for edible items in water, mud, soil, wood or snow.

Birds also have a truly amazing memory. If they knew the location of the food before the snowfall, they may simply be remembering where it was. A lot of birds make hundreds of food caches that they then can go back to later and their memory of the locations seems to be far greater than mammals seem to be capable of. Every study I have seen that pitted bird memory against squirrel memory has shown the bird substantially better. Btw, the human grad students were, compared to the squirrels, dumb as posts in their memory ability.

In addition to the real food caches, the birds will also make numerous fake caches. If the bird thinks it is being watched, many birds will pretend to hide food and they remember the locations of these fake caches as well.

Just goes to show that having a fantastic memory does not mean the same thing as being intelligent (I am presuming of course that the grad students were in fact smarter than the squirrels who consistently outperformed the humans in finding seed caches).