Television will be the death of movies! The Internet will be the death of bookstores! Yet bookstores and movie theaters are still full on Saturday nights. I have a nasty Amazon habit, yet I still go brick & mortar to pat the books.
Similarly, online ordering will never replace a knowledgeable tack store or feed store. Before I buy, I want to feel the bristles on the brushes and try on the britches. Also, some things don’t ship well: bottles of liquids, bulky buckets, feed. The Internet works when you know exactly what you want &/or the item is too specialized/exotic for local stores to carry.
For example, my recent online, equine purchases:
Specialized – A stack of horse agility books to inspire our groundwork exercises [Retail].
Specific – Supplements. Yeah, I know the arguments that supplements just make expensive manure. I even partially agree with them. However with her fairy dust, a) Mathilda has sounded a little less like a bag of castanets falling down the stairs & b) she’s made it this far. We aren’t changing anything now.
Scarce – Saddleseat britches [Day 1, pictured]. No saddleseat vendors near me.
OTOH, I have had no luck at all with online classifieds, which is ironic as Previous Horse & Mathilda both came from newspaper classifieds back in the day.
How has the Internet changed your horse (dog, cat) shopping?
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Gratuitous Kitten Pic
Virtual Brush Box 
It’s definitely changed it. I buy most of my stuff online. The exception is food and what I find from vendors at competitions (treats mostly, occasionally something else).