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Two notes #1 20 feet is going to cost you more per foot that 100 feet.  #2 All prices are relative to Your market ie Omaha is less expensive than St Lious.  Here expect to pay on the 100 foot job $5 to $6 per foot of gutter (5" aluminum) plus the $4 to $5 a foot for the downspouts and $15 to $20 for soffit and facsia covering ie vinyl soffit panels and painted or vinyl clad aluminum covering the fascia.  In the trade a soffit & fascia job. 

Jim Casper Gutter & Gutter Cover contractor in Iowa & Nebraska

ps see my website for blogs on gutters & covers

Not knowing what type of eaves (the lower edge of the roof) you had before the new soffits were intalled I have to guess what might have happened. If you had closed eves (no soffits, just rafter tails with blocking between) before as was done on some older homes it is possible they removed or drilled holes through to the attic. When this was done there should have been a baffle installed to direct the air flow up and over the insulation. This would only be possible for the soffit installer to do if the wood blocking was removed and not just had holes drilled in it. If the insulation contractor did not go all the way to the exterior wall that could very well be the cause or it he did not make sure the insulation was pushed down to make contact with the ceiling material. If the house was never cold before I would bet the problem is at the eaves. You should call the insulation company for an answer.

Don

The ice build-up in the gutter should not, provided they are properly attached and solid, rip out the gutter.

When you get snow slides and large chunks of frozen precip that let go and slide down the roof with velocity, those are what tear off the gutters and create damage.

If you are concerned about the snow load, a snow rake and/or a proper roofer can remove some of the accumulated snow. 

Some ice damming is unavoidable in the correct conditions but I would urge you to look into proper ventilation of the roof and air sealing and insulation.  This will reduce your home's inclination to form these ice dams in the future. 

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