Bathroom vent question

I live in Montreal so we have very harsh winters, last winter we had an issue of leaking bathroom vent from ceiling. When I opened up the ceiling I saw ice forming around roof ceiling. From outside the vent was buried under snow. I went outside cleaned that as well. They told me I had this infiltration because of ice build up around vent up on the roof. They advised me to clean it. But somehow I see almost no one doing that during winter. I am stuck between the idea of using soffit to divert vent outside but since the attic is very narrow it is difficult. I want to use the existing one but I dont like the idea of cleaning after every snowfall and possible infiltration because of ice buildup around vent exit. I will attach some pictures to better explain my situation. My understanding that I have two sheets of plywood on roof somehow deteriorated because of infiltration. I also noticed a wasp nest close to opening on top close to clapper inside the vent.

What do you suggest? My idea is to fit a pipe inside this 4" diameter vent hole and attach with insulated pipe and seal around with expanding foam.

I am also stuck between the idea of calling a roofer to change the vent exit on top or ask him to divert under soffit.

When there is rain there is no leak only winter when the exit buried under snow.

Maximum brand exhaust hood. Made for your climate,doesn’t have this issue.
Don’t exit through the soffit,your soffits should be vented and the moisture just comes right back in.

I just checked the product “Maximum”. I have the same thing! But I noticed first time that the ice was between insulated pipe and plywood also the insulated pipe was attached to ceiling with duct tape. My understanding is the connection was not airtight and there was a leak (on the left on the image) thats why there was a black spot.

Airflow was weak also air was leaking between fixture and plywood. This is my theory. Since I know I have the right product I am planning to fit 4" pipe into fixture seal it tight. Also I am planning to put foam in between outer edge of fixture and pipe this also should provide some insulation. But I dont know how to attach insulated pipe to ceiling (not duct tape for sure) I believe it failed in first place thats why there was a air leak. What is your suggestions? Thank you.

There should be a flange on the underside for you to attach the insulated pipe to.
Since there isn’t, you need to remove the hood,fix all the rotten wood and install the proper flange.
Hose clamp the insulated pipe to the flange,make sure the pipe itself is a relatively straight run in the attic for airflow and that the fan itself is strong enough

I am so afraid to touch to roof. I noticed the flange come out with old insulated pipe along with nails etc. Is there any way that I can fix this without flange and redoing the fixture on the roof?

If your afraid to touch the roof,hire somebody. Safer and if they kn what they’re doing likely a better result.
Make sure they’re licensed and insured.

Somebody offered me to direct the pipe to the side of the house, this represents almost 22 feet of piping, the other one told me this could be problematic since 22 feet is long and could cause lint and condensation problems.

I called Maximum company they said the connection has to be airtight (my case wasnt), if not the leaking air would create a “hot spot” and cause ice formation around fixture (on the roof)

I looked at Maximum website for the model CT-4, surprisingly it doesn’t need a flange. I am thinking to re-use the fixture since it doesnt need to fix (I suppose) But before apply (spray) antifreeze around the perimeter to prevent mold growth. On of the roofers that I talked offered this. Is it feasible?