I just purchased a 2013 Honda Odyssey. Previous one was a 2004. I have winter tires from the old Honda (225/60R16) and wondering if they would be compatible with 235/65R17 size for the 2013 model?
Nope. The R16 means it's a 16 inch rim, whereas the new one has a 17 inch rim. Otherwise, it would have been okay for regular driving, but the difference in rim size makes it a no-go.
If they could fit, you may have experienced a lack of power because the new tire has a larger circumference, but it may have been small enough to not be a major problem.
The old wheels are 16 inch and the new 17", but, the difference in sidewall profile compared to width means you would have lower gearing so would have to rev engine higher to achieve same speed, plus, speedometer will read slow, but not by much. Fuel economy would suffer. If the 'old' tyres are still good you would probably be better off selling them and putting money towards correct size
Short answer: it doesn't seem like there's a good way to use your old tires on your new car.
You don't state in your question whether the winter tires you have from your old car are mounted on a set of wheels or if they are tires only.
If they are bare tires, you cannot mount them on the wheels from your new car. Your old 255/60-R16 tires only fit a 16 inch wheel (thats the R16 part of the size), while your new car has 17 inch wheels.
So what if you had (or were willing to buy) a set of 16 inch wheels for your snow tires? Could you then use them on your new car? Unfortunately, that looks like a NO also, for two reasons.
First, it's quite possible that no 16 inch wheels will fit your new car. TireRack.com doesn't list any 16 inch snow tire packages, or any 16 inch wheels that fit the 2013 Odyssey. They list only 17 and 18 inch options. This leads me to believe that 16 inch wheels won't clear the larger brake calipers of the new car.
Secondly, the rolling diameter of your old tires is too small for your new car (roughly 8% smaller than what came on your new car). This would decrease your gas mileage and your speedometer and odometer would be inaccurate.
Looks like you'll need new winter tires for your new car.
I don't know where you live (your spec could be different) but with a quick google search it look like they would fit. Here they have 16inch wheel as base one and 17inch as optionnal wheel.
If the tire are already on wheel I would try to install one in the front and see if it clear the brake component. If the tire aren't on wheel I would go to your dealer and ask them.
Most likely 16inch wheel would fit and be ok... since the car has those from the dealer (if you don't take the 17th option)
edit: This other source seem to say that the wheel are 17inch and don't talk about 16inch. Your best bet would be to check if the wheel fit or call your dealer.