Say I was a mage, and my spec was Frost, and the talents I chose weren't made for raiding, would that make the raids harder?

Yes, talents have a effect on how you raid. Having the proper talents will allow you to have higher dps, tank better or heal better.

It would undoubtedly make the raid harder if the rest of your members were not doing fantastic dps. It can go unnoticed if the other members of your raid are exceptional and make up for your lacking in dps, Still, with a better spec encounters would go down faster for your group and the extra thousands of dps could easily help your raid to beat an enrage timer.

Chances are your dps would be lower than everyone else and you could be kicked especially if its a pug.

If you are going to PvE as a mage i would advise going arcane, or fire if that suits your style as Frost just is not as viable in a PvE environment.

If you are interested in finding any good specs i suggest looking up some of the top raiding guilds mage's and their spec. (try paragon mages, they have both arcane and fire specs which are for top end raiding) For additional help on mages, rotations.. optimal gearing.. i suggest taking a look at elitistjerk forums and maxdps.com for sorting out priorities and the best way for you to gear.

The proof that your talents make a difference is easily testable on dummies, and quite often makes sense when some talents clearly boost the damage you do with the crit chance you have, procs..etc.

Good luck fixing your talents and raiding smoothly.

Frost is mostly PVP for now. In 5 man dungeons be whatever, but in a raid fire has the most on the go spells, for example fight with a lot of movement involved fire is king. Raid encounters where you can stand still for a length of time arcane will blow fire out of the water. Ultimatley, dual spec fire / arcane unless you PVP in which case frost is a good idea to have as a back up.