Advice on Skyrim build

I've been playing skyrim for a while I'm a level 46 with mostly all health and stamina raised and a little towards magicaka. I've been wanting to make a mage for a while but can't help but play the stealth role. Could I just start adding magic to my thief and just go from there or is this something I really need to dedicate to from the beginning?

You can switch with not problem or even really caring. There is a reason I say Skyrim you character role is Mr. Perfect that choose to focus on something.

It will probably be a lot easier to start from where you are. You can get everything you need from winterhold

Note that spells cost less magic when you get better in the spell school.

-so, those destruction spells you cannot now cast as they cost too much magic, will become cheaper to cast as you train in destruction.

And of course, perks in the destruction tree will make spells even cheaper to cast.

I usually start Skyrim by putting lot of level up points to magic on the early levels. This way I can start casting spells from every school very early, and thus raise my level in each magic school real fast.

Good way of getting better at magic is by casting summoning spells continuously as you travel. Destruction spells need target to raise your skill level, but spells like summoning do not.

I_n that regard, it is always good idea to buy spells that do not need target to cast, such as the candlelight spell, so you can keep casting them continuously to raise your levels. One such spell for each magic school, and youre on your way to become master mage.