Yes, you can do that -- if you know your horses respect hot tape and you keep it hot. How big are the pastures? Obviously, the smaller the area is, the more often your horses will "encounter" the fence.
Your most secure bet is to run hot tape on capped t-posts -- which can be a pain to drive in, so expect a serious shoulder workout unless you pay someone. And do it when the ground is soft. But it can work very well, my horse lived in that for about a year before wooden fencing was built and had no issues as long as as the fence was kept tight and hot. He would run through saggy bits, even if they shocked him, so you need to keep it all in good repair.
Fencing is very very expensive, so if you really want to fence it, find out the acreage you'd want fenced, get a quote from a couple fencing contractors with the type of fence you would want (wood, vinyl, diamond mesh, whatever) and then use that as your bargaining chip. It's going to be more than a couple thousand, I'd bet, unless it's just a very small place. Don't sell your horse's safety short, as I'm sure you will not! :-)
You might also be able to use lack of shelter to drive the price down -- in many states it is techincally illegal (although not always enforced) to have livestock with shelter, so that could be a bargaining chip.
If it was me, this is exactly the way I'd go about it -- drive price down, run hot tape inside the wire, then slowly remove wire and replace with appropriate fencing. Good luck!
ETA -- Remember you, the buyer have ALL the power. Don't let emotional want drive you. Be prepared to walk away, but leave an offer on the table. You'd be surprised how often buyers change their mind about an offer they initially reject, especially in today's crappy market. Don't let anyone (even yourself) rush you into a deal until you are fully satisfied.
Solaris -- 16 hh Appendix Quarter Horse = MY DREAM COME TRUE!We Are Flying Solo