I am putting a new roof on with new gutters. I don't have any soffits, poor workmanship. The house is over 50 years old. I am getting mixed answers. 2 people said yes to gutters but one said gutter covers would help stop the ice dams and the other person said he didn't like them because he felt they would increase the chance of ice dams. PLEASE HELP!!

Gutters and gutter covers have little to do with ice dams. They can contribute to the ice problem but really it's a matter of not having enough airtightness and insulation in your ceiling at the eaves or exterior walls.

Green Building Advisor article on Ice Dams

Since you don't have soffits (overhangs) you have no ventilated soffit which means step 3 in above article is not possible. I would absolutely look into steps 1,2, and 4. All of which should help your situation.

Now is a great time to implement 4 because of the roof work. Steps 1 and 2 should have the added benefit of increased comfort and reduced energy costs.

I haven't answered any questions in awhile and hope you can rate this positively if it helps. Thanks!

Greenie from me!
The part about pot lights made me cringe, but mine at least are below the attic, in a kitchen soffit. What gets me are all the exhaust fans we have going out the roof, and watching the warm air melt snow and cause massive ice and dripping icicles on gutters, whether there are soffits or not.
No soffits doesn't have to mean poor design.