On a motor driven vehicle radials on the rear and bias on the front is the only mixed combinations that tire companies like Michelin and Goodyear state is okay BUT not advised. Reason being that bias tires don't grip as well. Put bias on the rear and radials on the front and the vehicle oversteers. The bias ply on the back end passes the front when the rear end looses traction before the 'grippier' front radials. Put radials on the rear and bias on the front and the vehicle understeers which is generally the lesser evil compared to oversteer. Not ideal, but at least the rear end stays where it is supposed to be. Similarly it is best to install new tires on the rear axle, not the front. Reason again is to get the best gripping tires on the rear so the rear end stays where it is meant to be.
Word from Goodyear on this....
"When radial tires are used with bias or bias belted tires on the same car, the radials must always be placed on the rear axle. Never mix radial and bias-ply tires on the same axle. When you select a pair of replacement tires in the same size and construction as those on the car, we recommend you put them on the rear axle. A single new tire should be paired on the rear axle with the tire having the most tread depth of the other three."
You can find that quote on
this page.And since they adamantly state to not mix types on the same axle I guess I'd change my tune on my previous "maybe it is okay" on a trailer. I guess maybe okay at very low speeds in an absolute emergency. So I'd now say never cheap out and save a few bucks by purposely buying a bias for a spare tire.