I like to be there in person so I can see it for myself. Especially when I buy a saddle. I will test ride in it and also see if it fits the back of my horse correctly. If it is a halter, boots, etc.. and I know the company I will order it online!
Usually from the tack stores in town but depending on what it is I order it online.
I buy it from local tack stores so I can see it before I buy it in case it's totally different on the internet.
If I can, I like to purchase in store, but I live in a small city with a single (very small) tack store, so online in usually best for me if I need something.
I have never purchased items such as helmets, saddles or riding boots online though, but bridles, saddle pads, breeches (I email the store and ask for specific measurements), etc. is usually fine. There's often good deals online if you can find a tack store with affordable shipping! :)
I prefer to shop for sizing purposes. For example, if my martingale broke, I can bring it with me & compare the sizes so I don't end up buying something that doesn't fit properly