Assuming the cat-hole is the preferred protocol for waste disposal in the area you are backpacking, what should you do when the soil is buried below A LOT of snow, and/or frozen?
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If the depth of snow and/or the ground being frozen prevents you from burying solid waste below ground level by at least six inches, then, in the spirit of leave no trace, you should carry it out. Use a biodegradable (e.g. cornstarch-based) bag to pick it up and then pack it in a sealed plastic container. For obvious reasons the container should only be used for that purpose and disinfected when you return home.
Burying solid waste in seasonal snow is not sufficient. Whilst in the snow, the cold will slow biodegradation and during a melt the result will be as if you had never buried it at all. In larger or permanent snowfields I've seen the advice of disposing of solid waste at least 200 metres from camps and trails, but, I'd still prefer carrying it out to leave no trace.
Also, the advice from local conservation bodies will vary by region depending on the local ecology etc., I'd treat this as the minimum acceptable way of dealing with waste.
There is really two different answers, one if you are dealing with glacial ice, and one for seasonal snow.
For seasonal snow and for solids, your best bet is to bring biodegradable bags, pack your waste in as deep a hole as you can manage, and you should be fine. By deep, I mean a few feet at least, or better yet, a deep natural crevasse.
For liquids, pick a designated area to dispose of your waste properly, trying to minimize the space. Try to pick an area that someone isn't likely to try and make water from the snow, especially if in a popular back country area... Bushes, trees, etc should be fine if you can manage.
For glacial areas, use the same guidelines as above, but in general, you might consider packing it out. Denali in particular, and many other mountains, require packing out solid human waste, and liquid waste in many areas.
I would dig a deep hole in the snow - and then cover it up again, because when the snow melts, the waste will decompose fairly quickly with warm temps and water, it'll break up and disperse.
If it is practical, find some dead branches, leaves, or even rocks, and cover it up and then put snow back on top of it.