Charlie Brumbaugh's answer is fairly comprehensive about the dangers. I will address some ideas on how to deal with this sort of trip.
A: Take an avalanche safety course. It will teach you something about how to recognize possible danger zones.
B: Take a set of avalanche beacons, probes, and shovels.
C: When in a high hazard area travel far enough apart that losing more than one member in a slide is unlikely. Turn your beacons on transmit.
A: Take equipment that will allow you to camp without a hut. This means winter rated tents, and probably better sleeping bags than if you are planning on using heated huts.
B: Spring storms can make you immobile for some time. Carry two days extra food, and stove fuel.
High water hazard
A: Travel during nice weather or obtain pictures of the region before you go. Examine streams to see if they have history of serious high water. (A local mountain stream, Mumm Creek is dry or a trickle in summer. However it has a flood plain 100 m wide scoured clean of vegetation. Clearly it has serious floods at least every few years)
B: Plan alternate routes that will eliminate major stream crossings.
C: Carry or be prepared to cut walking sticks to aid in stream crossings. Note that conventional walking poles are mostly for balance and won't support your weight.
D: Carry a rope for rigging a line across streams to aid in crossing. You may use this rope on high angle slopes too.
E: Be prepared for the entire group to be wet up to the waist, and for at least one person to be immersed in the stream.
F: When crossing a stream, undo your waist buckle. You do NOT want to be struggling with this if you fall while crossing.
A: Use snowshoes. The metal and neoprene ones work well in spring conditions.
B: Change your day up. Camp early. Half the party, carrying minimum stuff then breaks trail for the start of the next day's travel. Traveling without a pack is much easier and faster. This trail will set overnight and be easy walking the next day.
C: Use a buddy system. Everyone has a partner. Partners look out for each other.
D: Learn to recognize hypothermia. Wet spring snow + wind + fog is prime hypothermia weather. Game out situations of what you would do if you discovered you had a victim. Factor hypothermia checks into your buddy system.
E: Everyone carries a whistle. Agree on a whistle code. The one my groups use is:
* One long "where are you"
* One short "here I am"
* Two longs "Come to me"
* Two shorts "I'm coming"
* Three longs "I need help"
Note that in summer you want whistles that do NOT sound like marmots or pikas. This caused enough confusion one trip that the ones were changed to fours.
A: Carry both printed maps and have maps loaded on your GPS. Visibility may often be limiting. Having two GPS's isn't a bad idea. Carry sufficient batteries. Maps and GPS should be carried by different people so that the loss of a pack doesn't mean you're lost.
B: Unless you are experienced with glacier travel stay off the ice. This is another area where I recommend taking a course.
A: I have a Garmin Inreach. This allows me to send and receive text messages anywhere in the world. My wife can send me a daily weather forecast for the region I'm in.
B: A sat phone is another option, but is expensive to rent and to use.
Spend time gaming out scenarios. If you are leader part of you must be constantly assessing hazards, and what-ifs. Talk about these in the evening. They are more real right after, and your group can fill in the situation from what they observed.