Will I create any kind of problem by hooking uo a battery saver to my 1990 Reatta while it is stored over the winter?

no

I use the "Battery Tender" brand of charger on my antique/classic vehicles as well as my trailer batteries and tow vehicle.
The Battery Tender is an intelligent charger that keeps a battery charged at a much higher level than a conventional auto battery charger and many trickle chargers.
I have been using this charger for about 8 years now and not one of my vehicles has yet to have a battery problem and/or not start.
These charger are more expensive than other chargers on the market but they simply work very well for me.
BTW, they also make a water-proof model that can be used outdoors.
They also make 20 foot extension cords that I use for my tow vehicle and trailer.
That allows me to keep the charger in the garage (it is not a water proof model) while keeping the batteries charged in the tow vehicle & trailer outside in the driveway.

FYI, I do not work for the company that makes this product nor do I sell it. I am just a very satisfied, long time, customer.

I also use the "Battery Tender" on each of my Buicks all year round as they're not driven weekly (not at all in winter). Really saves on car batteries. They're self-monitoring and go on and off as they fully charge the car battery. So, I don't need to worry about over charging.