When U-Haul first started renting trailers..Disc brakes were pretty much unheard of on passanger vehicles.
I speak from experience on this one because my '65 Mustang has front and rear (non power) drum brakes.
If you tow 45 mph there is a good chance you can react and stop a 1000lb trailer with some "pumping" and good reaction time, but it's a possibility that something could go wrong too.
If you stab and hold the brakes on the older cars you will get to a point (quickly) where the brakes hardly respond at all.

The posts about wheel bearing, tire size, and handling are all very relevant but don't forget that the modern braking systems are much different than the old ones.
I hardly ever drive over 60 in any kind of traffic when pulling with the '65 Mustang. It's just too scary to think about.
I like the car and I like the trailer just the way they are.
BTW, an upgrade to front disc brakes is in the future plans.
