I would do 2 things. First install spring bronze weatherstripping around all sashes. It can be purchased at kilianhardware dot com (no, I'm not affiliated with them) or an older style hardware store can usually get it. Then I would make/have made wood storms that are single pane as well. That should work for your wife style-wife (and I agree with her). If you can make the storms, you'll save a ton of money; however having them custom made won't be a super huge expense....they'll be tons cheaper than new windows. Skip the plexiglass - that will look awful.

Your wife is right about not replacing the windows. Get yourself a copy of the book Working Windows by Terance Meany. It's been out of print, but is due to be reprinted this spring. It is the best book for keeping and maintaining old windows. Your local library should have a copy, too.

These solutions won't cost you a ton of money, either and you and your wife can do them yourselves.

Storm windows will make a marked difference because what you may be feeling as a draft is actually convective air movement within the house as it falls down from hitting the cooler surface of the glass. (I'm not downplaying the need to add good weatherstripping as mentioned above, but trying to add weight to the suggestion that you use storm windows, as well.)

BTW, many people think that aluminum triple tracks are the only storn window out there, but that's not true. You can have beautiful wood frame storms made that will look just fine with an old house.

In addition there are the so-called "invisible storms" which are metal framed but designed to blend in with the existing window frame. These can be pricey, and being metal framed they are not as much of a thermal break as wood-framed storms are. And they tend to be fixed in place year-round, though some have screen panels.

For a short term solution I also can suggest a product called Windo-therm, which is a metal framed, double layer of stretched poly film mounted indoors. These (in spite of the fact that the "glazing" is made of shrink wrap film, albeit quite high-grade shrink film) are not inexpensive, but they do a good job. In fact, in my never ending work on my own windows, I have a couple of these window panels that I rotate from window to window as I take out the sashes for refurbishment. In order to be able to work year round on my northern NY house I sometimes, like today, have nothing between me and -5F outdoor temps except a Windo-therm panel. Frankly, a well weather-stripped temporary WT panel is less drafty and keeps my rooms warmer than my un-updated primary windows with aluminum triple tracks. Taking out my sash to work on them and installing the temp WT is an improvement. WT panels are definitely not the same thing as plastic film you buy at hardware stores, they're much more formal, and work much better, and are quite reusable.

I'm not sure what the WT web-site is these days, but I expect you could Google it.

HTH,

Molly

Your big box store will have (in season) a poly film for instant storm windows to be used in or out. The stuff comes in a box with double sided tape, easy to put up and take down.
We are using it in our kitchen while we consider our remodel. It is clear enough that if you have curtains on the sides, hiding the edges, you cannot tell it is film.
When the wind blows and the film bows in (and you can't feel the draft!) you will be able to see it.
You might also consider interior storms. They work well and are easy to install and take down.

I've linked below a site I found with instructions for DIYing interior storm windows that mostly friction-fit into the frame instead of requiring the mounts that most interior storms need. Were I to go to the work of building them I would probably use a good clear plexi instead of plastic film for durability and a nice appearance, but I think it's a pretty good design overall. If painted or stained to match the trim they'd probably disappear pretty well, especially if you have window treatments.

Here is a link that might be useful: DIY interior storms

I have an old magazine with pictures of inside shutters on some tall windows. They sure look great I've dreamed about them for years. I don't know if this would be something that would work but if you're interested I'll try to scan a picture