Dirr's does not list cuttings as a propagation method for P. parviflora. But there is some discussion on the P. strobus entry saying that it is variable by cultivar and specimen.
I know that Zuisho JWP are propagated by cutting so at least some varieties work. I've seen pots full of white pine cuttings in Boon's yard before but I don't know if they were successful or not and I don't know the cultivar.
Default method for me would be early November, remove needles down to a reasonable amount, cut at an angle, use pearlite and sand. Rooting hormone in the stongest concentrtion you can get. Protect from cold over the winter (like keep them inside under a grow light and timer.) and high humidity and bottom heat are generally very helpful.