Не будь снегоступов, мы бы поскользнулись на насте.

No. Although будь is formally the singular imperative of быть, in this sentence не будь + genitive is a fixed conditional expression.

Here it means something like:

• if it weren’t for ...
• had there not been ...
• if we didn’t have ...

So Не будь снегоступов is not telling someone don’t be snowshoes or anything like that. It is an idiomatic, somewhat literary way to introduce an unreal condition.

Because the construction не будь + noun requires the genitive.

So:

• снегоступы = nominative plural
• снегоступов = genitive plural

This is just how this fixed pattern works:

• Не будь тебя, я бы опоздал.
• Не будь дождя, мы бы пошли гулять.
• Не будь снегоступов, мы бы поскользнулись...

Since snowshoes is plural, the genitive form is снегоступов.

Russian has more than one way to express an unreal condition.

A more neutral version would be:

• Если бы не снегоступы, мы бы поскользнулись на насте.

But Не будь снегоступов... is a shorter, more compact alternative. It often sounds:

• more literary
• more formal
• slightly more dramatic or stylistically marked

So the sentence is perfectly grammatical, but it is not the most everyday conversational wording.

In Russian, the conditional particle бы does not always need to appear in both parts of a conditional sentence.

Here, the first clause already shows the hypothetical idea through the fixed pattern не будь + genitive, so the actual conditional marking appears in the main clause:

• мы бы поскользнулись

That is enough to give the whole sentence a counterfactual meaning.

So this is normal:

• Не будь снегоступов, мы бы поскользнулись...

You would not normally say:

• Не будь бы снегоступов... ❌

Because будь is not agreeing with снегоступов here in the usual way. In this construction, не будь functions as a fixed form.

So even if the following noun is plural, you still use:

• не будь снегоступов
• не будь друзей
• не будь этих мер

In other words, будь stays the same because this is an idiomatic expression, not a normal imperative agreeing with the noun after it.

A fuller version would be something like:

• Если бы не было снегоступов, мы бы поскользнулись на насте.

Or, depending on context:

• Если бы у нас не было снегоступов, мы бы поскользнулись на насте.

So Не будь снегоступов... is basically a compressed version of that idea.

This is useful to know because many learners understand the sentence more easily once they mentally expand it.

Because поскользнуться is a perfective verb meaning to slip once / to have a slipping incident.

In this sentence, the idea is a completed hypothetical event:

• we would have slipped

That matches the perfective very well.

Compare:

• скользить = to be sliding / to slip repeatedly / to glide
• поскользнуться = to slip once

So мы бы поскользнулись means we would have slipped, not we would have been slipping.

На насте uses the prepositional case.

That is because на with the prepositional case usually expresses location or position on a surface:

• на столе = on the table
• на льду = on the ice
• на насте = on the snow crust

Here the idea is that the slipping would happen on that surface, so the prepositional case is natural.

Наст is a specific winter word. It means a hard crust formed on top of snow, usually after thawing and refreezing, or after wind and compression.

It is not just ordinary snow. It is that firm, crusty surface you can sometimes walk on or break through.

So на насте is more specific than simply на снегу.

This is the kind of word native speakers know, but learners may not meet it early unless they read nature writing, winter descriptions, or outdoor vocabulary.

Yes, absolutely.

A very natural alternative is:

• Если бы не снегоступы, мы бы поскользнулись на насте.

This is probably the version most learners should actively use first, because it is more straightforward and more common in everyday speech.

The original Не будь снегоступов... is good to recognize and understand, but it is more stylistically marked.

Yes, that is also possible.

Compare the nuance:

• Без снегоступов мы бы поскользнулись на насте.
  = Without snowshoes, we would have slipped on the crust.
• Если бы не снегоступы, мы бы поскользнулись на насте.
  = a clear standard counterfactual
• Не будь снегоступов, мы бы поскользнулись на насте.
  = more compact, literary, somewhat elevated

All three are possible, but they differ in style.

It is grammatical and natural, but it sounds a bit bookish or literary.

In casual speech, many speakers would be more likely to say:

• Если бы не снегоступы, мы бы поскользнулись на насте.
• Без снегоступов мы бы поскользнулись на насте.

So the original sentence is the kind of thing you might see in:

• written narration
• literature
• descriptive prose
• more polished speech

It is useful to understand, but not necessarily the first version a learner would choose in conversation.