<<> LdP has "hima" for "winter", it's me who suggested it to Dmitry ! :-)

<But why winter? It's a different thing than snow. I would prefer "zima", 
which is a real, modern word.

Because Dmitry sought a word for "winter". I think LdP has already "snega". 

> And Sambahsa has both "winter" and "ghim" (this later from PIE).

<<Are they synonyms?

Yes, they are. 

> Sambahsa has other words from roots you've mentionned :
> varf = snow-covered mountain top

<<Isn't it too specific? You could use compound word like snowpeak. It 
would be immediately understandable and burden less memory.

I suppose we understand what is meant here. Maybe "pic de neige" would too much like "ice-pike" in French. 

> eger = assuming that
> agar = in case that

<<Eh...? So, basically, the same word family has produced two separate 
word instances in Sambahsa with slightly different meanings. And both 
meanings are slightly off compared to the original.

Why not ? That avoids répétitions in translations. 
Two instances from the same root in the same language are not rare in some natlangs. Ex : French "cheville" vs. "clavicule", "chancre" vs "cancer", etc.