Hi, I've been lurking and reading these forums for awhile but just literally made an account so I could share my thoughts on this -- because I'm one of those "crazy horse girls" myself :D (Yes, we all know about that rumor and find it pretty funny!)
It's true that horses can be prohibitively expensive, especially in certain parts of the country. I must be one of the less crazy horse girls because I recently passed up an opportunity to spend $20k on the most amazing horse I've ever ridden (who later sold to a very wealthy family for $50k), not because we didn't have the cash, but because the upkeep costs would have been a $1500/month budget hit. That's more than my mortgage!!! I took a voluntary break from riding instead. Key word: VOLUNTARY. I was really upset at losing the horse of my dreams, honestly, and even being in the barn was pretty heartbreaking. However, if my husband had pushed for it, he would have had hell to pay. I don't think I would have left him, but we are young and just got married and haven't raised SIX boys!
My guess is that if you can afford to keep multiple horses on your own property, at least if you keep them in quality conditions, you live in a lower cost of living area. This also probably means that horse board is cheaper in your area. My suggestion is that you do some research on board prices at good barns with riding arenas (and indoor arenas, if you live in an area where one is required for winter riding). Compare those costs to the cost of keeping the horses at home, the bigger mortgage, bigger transportation expenses, etc. If/when you go to your wife, it might be helpful to have this information already. Just don't ambush her like "We would save $500 a month if you'd only give up your dream lifestyle and only hobby!" because that's not going to end well.
If she's not riding, but says she wants to and has ridable horses at home, there's a reason. She's likely either overwhelmed with the daily care of the horses and other aspects of life or afraid to get back on after not riding for a long time. Both of these situations will be helped by keeping one or possibly two of the safest/sanest/most ridable horses at a boarding barn where all she has to do is show up, brush, tack, ride. Honestly one horse is all most people with full time jobs and kids can handle, especially if they want to improve or even maintain the quality of their riding. It is a sport, and it does take practice -- 3+ good longish rides a week, at least in my discipline and level.
EDIT: If anxiety/fear about getting back in the saddle is a factor, you should also make sure to pick a boarding barn with a good instructor/trainer and solid lesson horses that she could start out on, especially if it's likely that her horses will need some retraining before she can feel confident on them. A good trainer can do wonders for a rider, not only in skill level but in making you actually want to ride.
Perhaps you can approach it that way -- you want to see her actually enjoy her hobby, not just view it as another chore. The goal should be to simplify both of your lives to a point where you can both enjoy the things you want to enjoy, and if keeping horses at home is just adding another layer of stress and chores, then maybe she could think about paying someone else to do the chores part of it so that she can simply have fun and enjoy her hobby.