Why hot water pipes get frozen first, I don't think so.
I think that the first step is to check for "air leaks" inside the house. Houses expand and contract continually with the seasons and cause separations between walls inside and outside.
Using caulking it could fix the problem just by sealing all "cracks" found outside, around windows, doors, between levels like basement and first floor if the house is not whole wall brick, etc.
Usually, the main problem is cold air leaking inside the house and freezing the pipes.
Insulating pipes is next if no air leaks are found. Also, if this is possible, to insulate walls, but this is a major job.
The electric heat wrap is mostly for pipes running "outside the house" or exposed to open crawl spaces under the house. I won't recommend them for heating pipes running inside walls or ceilings.
Check for leaks first, which is the easiest step. Caulking cost about 5 bucks, the caulking gun another 5 bucks, a caulking application lesson for free in Youtube, and the attitude of doing it by yourself. Otherwise a handyman is the cheapest choice after.
Yes, you must call the plumber, I think he will understand the problem very well and able to resolve it.