I have read many articles on frozen vent stacks and the most recommended fix is to try and insulate the pipe as it travels through the attic. When I went into the attic with insulation and plan, I found the vent stack comes from the roof to the top of the ceiling joists and runs horizontally in different directions above the insulation. Is this allowed by code? Is there any sense insulating the vertical rise since most of the pipe runs horizontally all through the cold space anyway. The main trunk is 3" PVC but it also branches off with 1.5" PVC taps. It does not appear to have any fall to it, if it does it is very slight.
Every winter my pipe freezes up and gases enter the home through the basement toilet and I really want to fix this properly once and for all.

can you tell exactly where it is freezing?
is it the vertical section just as it exits the roof or do the smaller branches freeze as well?

unfortunately I do not know. My roof is very steep and two storey and covered with snow so I can't get up top. I tried a lazer temp meter from inside but it red 22F at various spots and I tried tapping it and I could not tell where it was solid vs hollow. It is about 20F outside so relatively the same as the attic space.

should be 4" vertical pipe through roof to avoid the end of pipe becoming snow/ice bound

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"Measure Twice & Cut Once" - Retired U.A. Local 1 & 638

as suggested by my friend fron SC, increase the size of the vent thru the roof to 4 inch.
try to get at least a foot or two below the roof with the inverted reducing coupling.
this of course will mean changing the roof flange and possibly a roof shingle or two.
in the interim, you may be able to cut a couple tees into the smaller horizontal vent lines and install studor vents that would allow air into the vent system if and when the stack gets frozen over. this will keep the system from getting airbound and allow the toilet to flush.

I believe it will be 4 inch already... is the toilet your having issues with in a way different location than the other toilets in your house?? houw many vent penetrations do you have in your roof? my line of thought is: withought seeing it , I would believe is is vents by a 3" stack vent upsized to 4 at roof, and unless it is the only fixture on that vent, would ask do your showers tubs etc still drain?