Q:

Does position of nicht matter?

Suppose I want to say "I am not cold". I know this is "Ich bin nicht kalt". Is "Ich bin kalt nicht" also valid or is it incorrect? 
I ask because I often see "nicht" at the end of the sentence, but other times I see it before the adjective/verb/noun.

A:

Nicht generally precedes the item to negate.

Mir ist nicht kalt.

I am not cold.

Ich bin nicht müde.

I am not sleepy.
There is an alternative function of nicht however: as an interjection.

Sie haben es verstanden, nicht?

You have understood, haven't you?
It's not so common in Northern Germany but I hear it very often from Swiss German speakers. Oder is a replacement which is very common.
Maybe that's the nicht you hear ever so often?
And finally there's

Das finde ich nicht.

I don't think so.

Ich glaube dir nicht.

I don't believe you.

Sie gab ihm ihre Telefonnummer nicht.

She didn't give him her phone number.
which negates the whole sentence. English uses do not for the same purpose.

