I use cuttings of firm new growth (soft wood) taken mmay/june. & have very good results. (Raspberry/blackberry I use 0.1% IBA (rooting hormone) & for bluberry I use 0.8% IBA
IF you use hard wood cuttings then you will have some luck with rasberry/blackberry cuttings BUT in your area the house will need suplemental heating & bottom heat for the cuttings.

Softwood cutting will give you better results overall. This goes for just about every woody ornamental you want to root.
Personally, i would try softwoods with mist.