Hi I'm newb here, so please don't abuse me

Got question regarding Winter Tire and Rim and need a favor for the answer.
I've got a Toyota 99 Solara SE V6 with 4 disc brake, need to get 4 set of winter tire and steel rim. On my user menu, it appears that I have two choices of tire size:
P205/65R15
P205/60R16
Since I bough this car 2nd hand, it has
P225/65R16 right now... *Correction P225/60R16*
So when I went to the tire shop and as for a set of snow tire/steel rim, they told me since I'm using 4 disc break, I'll have to go with 16 inch tires, as 15 inch rim won't fit in as the position of caliper, from their previous experience.
However when I visit most of the tire/rim websites, it appears that I can go with both 15 inch and 16 inch. Is what they said true?
Thanks a bunch.