Here in Madison, Wisconsin, I transplant raspberries in the fall, and they overwinter fine. They grow like weeds in our yard, so I have to thin them every spring, or the patch gets so thick with canes that I am unable to get to much of the fruit. They also transplant well in the spring, before they have flowered, typically in April or early May. We have milder winter weather than Alaska, however. It gets down to 10 below every winter, and sometimes we see 20 below, but rarely any colder than that.

Plant them at least as deeply as they were in the in-laws garden, and do you have reliable snow cover in the winter?

Yes, theres usually a steady 1-3 feet on the ground with a nice thick sheet of ice underneath until April-May.

Then there's your protection; otherwise put some thick mulch on if there will be a deep freeze prior to the snowfall. Getting the soil moist before a hard freeze can help, especially if you have gritty alluvial soil, as it reduces the air content of the soil.