I know nothing about strawberry seeds so can't tell but probably works similar in their brain :)
If you don't get frosts and snow there, you could probably keep it outside all year round. Just make sure it doesn't get too much rain, and NO RAIN in winter when its colder (like below 10).
In summer it will love the warm weather and sun.
Most cacti can stand up to zero degrees and even below zero for short time if they are kept completely dry. The moisture is deadly when cold as they will simply rot.
If not - leave it some colder place for a month or two and do not water. Most will stop growing in the fall when they feel its getting colder. That's when I stop watering mine and will not water until around February when temp is starting to reach about 12-15 degrees. But I keep mine outside all year round.
Garage probably could work if cold enough and only after it stops growing. If it is warmer it will want to grow and with low light it will stretch and deform.
Do you know what cactus it is?
I think it is called a Euphorbia Lactea, but I'm not too sure as it's a while ago since I got it and when I google the name it looks different from what I have so, it could be anything.
We do get snow here, and it rains from November pretty heavy, I live near a river and that sometimes bursts its banks.
when I go to see my mum next I'll take a photo of it and send it to you so you can have a look, she's away at the minute for a week, otherwise I'd ask her to send me a picture :D
Ohhh Euphorbias are African cacti. I don't know much about them, so better don't do what I told you :P
I have two and one is outside with other cacti, gets the same treatment and it does bloom, and the other one is inside and never bloomed. They have tiny flowers - nothing special. But better read about it first before you kill it :p