The tournament rules have the following to say about alters:
3.3. Authorized Cards
Artistic modifications are acceptable in sanctioned tournaments, provided that the modifications do not make the card art unrecognizable, contain substantial strategic advice, or contain offensive images. Artistic modifications also may not obstruct or change the mana cost or name of the card.
The Head Judge is the final authority on acceptable cards for a tournament.
The last line would be the key element - I suggest you always ask the Judge prior to the tournament whether you're allowed to play a certain card, and be prepared for a no as an answer just in case (which means bring unaltered copies of the card).
Not all events labelled "FNM" by stores are sanctioned events, however, and as far as unsanctioned events go, you can bring whatever cards the other players accept.