Re: 15 inch spare to replace 14 inch??
For Trailer "tire sparing", its all about risk and impact. Risk of needing to use a spare? And if needing to use a spare, what is the negative impact?
I've been pulling trailers for 25+ years and never needed to use the trailer's spare tire. But, I always ensure I have a spare, wrench and jack - just in case I need it. Without a spare, I'd evaluate the negative impact without a spare. For example, trailing on Sunday and all local tire stores / auto shops are closed. Thus, I'd have to leave my trailer at side of road - until I get a tire replacement on Monday. If store is open, how far away is the tire store / auto shop - to fix existing flat tire? After all the + / - comparisons are added up, I always carry a spare with wrench and jack. And its spare is matching its other normal usage tire size and lettering. re: . ST205/75r14
If using different size spare, the trailer stance won't be level. The low side (due to natural gravity) will endure more load weight. And since axle isn't level, its lower side wheel bearings will be over stressed as well. Thus, hurting its spindle, bearings / races and seals. And, trailer brakes (if you have them) will behave differently as well. re: Pull to one side - because wheel's aren't the exact same physical size. With all this, I'd recommending using same size spare.
However... Since the 15" tire is for free, I'd take it "for free". Then, try to sell or trade this 15" tire for a proper matching 14" tires. Especially if this 15" tire is in great shape (and its under 6 years of its creation date).
Note: For more info about tire age and "under 6 years" warning, surf:
http://www.youtube.com/watch?v=pxlsKPCzjyw This 6 year limit applies to RV, utility and boat trailer tires as well....
Hope this helps...