Willows are very good at rooting, though I don't know that particular species. Here in Ladakh we propagate about 6 species of willow, all by cuttings, and putting them in cold ground is absolutely fine. We cut and plant in the beginning of winter or end of winter, but not in mid-winter because our soil is frozen hard. Of
course keep the lower end of the cuttings in
water or at least moist at all times from cutting until planting; If in doubt, cut off some of the lower end. Cuttings of any size work. Here we always use ones at least 2 or 3 cm diameter, with at least 45 cm (1.5 feet) below ground and at least 120 cm (4 feet) above ground to help them get a head start above browsing animals -- but pencil sized cuttings
root well too.
One thing is be sure to plant them while they are dormant. We always have some cuttings still standing in water as the spring warms up, and once their leaf buds swell, if we still plant them most of them die.