The world is brutal and cold

Question

Steal my prefix and perform a sacrifice.
Steal my suffix and venture all over ice.
Steal my infix and a shove from fatality.
Steal my whole and forget a part of me.

Answer 1

I think the answer may be:

SKILL

Steal my prefix and perform a sacrifice.

Remove ('steal') the prefix S to make KILL - an action necessary to perform an animal or human sacrifice.

Steal my suffix and venture all over ice.

Remove the suffix LL to make SKI - to move over ice or snow.

Steal my infix and a shove from fatality.

Remove the infix K and you are left standing on a SILL - one wrong movement (or indeed a shove) and it's potentially a lethal and long way down from the window ledge...

Steal my whole and forget a part of me.

Remove all the letters - i.e. lose a SKILL - and you forget how to do a particular task...

_{PS As for the title, I don't think this is relevant to the word itself - instead it's purely to set the tone for the rhyme: 'brutal' in the sense of a human/animal sacrifice or a fatal shove, and 'cold' with the imagery of ice...}