We live in New Mexico and have sailed twice to Alaska.
We bought hiking boots (inexpensive but sturdy ones from Target) and sprayed them with water-repellent. Boots are needed for rain/snow and especially for walking on trails with slippery rocks (protect your weak ankles).
Think of Alaska as seven days at WDW during the summer. Don't buy expensive but be prepared:
Dollar Store rain ponchos and a compact umbrella (the one you keep in your vehicle and use once a decade).