2013 Honda Odyssey Winter tires

2013 Honda Odyssey Winter Tire question
I am in the market for winter tires for my ‘13 Odyssey and have heard conflicting stories about using smaller rims for the winter tires.
One garage tells me no problem, I can go from the 17" rims now to 16" rims for the winters, and another tells me I can’t use anything but 17’ rims.
Can anyone answer this question?

The smallest wheel that car came with was 17". You might be able to use 16, but it might not clear the brake caliper.

For what it’s worth, Tire Rack’s wheel sizer does not think a 16" wheel will fit.