I have a very bad smell in winter from central HVAC. The HVAC specialist came and said that condensation drain line cannot go to the air vent of the plumbing, must go outside to gutters. My question are:
If there are too much rain, will water back up through gutters into house?
2. Will animals get in through the pipe that goes out?
3. Will pipe that goes into gutter freeze in winter?

There is also no p-trap that holds water. If they install P-trap, will we still need to get condensation drain line into gutters and not air vent of plumbing? What is the other solution of the bad smell?

I would visually look at the heating coils for anything laying on it?

Sounds like condensate drain no draining and you have a science experiment growing in the pan until it evaporates. But that would be most likely in summer not winter, reason for condensate drain not being allowed into air vent is because of sewer gas... which would enter as a result.

Drain would likely be 3/4" to 1" so animals won't enter but bugs might, but bugs could get in other ways too. Also water flows downhill so if you have water backing up enough to back into from gutters.. you have far worse issues to worry about as it would drip INTO the gutters from above them.

Being it's a condensate drain... you wouldn't have water dripping out in winter. Think about car windows on a cold day... thats why it collects when A/C is running, and why it won't when the heat is on... thats something to not worry about.

I think Stratmando is right... you need to find out what's going on or what might have crawled in and died, or otherwise collected.

Not unusually for an initial smell at beginning of the heating season, but that quickly goes away in a short time. Anything that lingers or continues is reason for a closer inspection.