I used to play a lot when I was younger but never bought decor/gear because I assumed you lost it once the wolf died, and since the wolf only lives to about 15-20 ish, I never bothered. How does it work? Do you just lose the gear?

Nope, you don't lose the gear!

You can use it on other wolves if the one who had been wearing it dies.

No, gear/decor is not lost when a wolf dies. It will return to your inventory once the wolf passes away so you can put it on another wolf. Gear/decor also has infinite uses so once you purchase it you will have it until you sell it or otherwise get rid of it.

How about in my Memorial Garden? Is there a way I can have the wolf keep the gear/decor?

Nope, dead wolves can't wear gear/decor (wouldn't it be nice if they could?)

They're also stuck with the same background they died with. I believe you are able to change their pose when they're in your memorial garden.