The thing with brushes, is, that we all have our favourite ones we like to use and that's why you will always get a mix of answers on here.
I personally like stiff bristles which dont splay too much but I found that out from trying various brushes particularly in my first Yr of using wfp.
Daz buys things and hates them, only to like them later 😂 so if your happy with the brush you've got and it still has life leftin it. Then I would go for a different one and build your experience and find which one suits you and your needs.
Haha, sorry for the waffle, but basically the answer is yes, it will be fine with cold