If I may offer some in the box - out of the box thoughts ....
Before the advent of carbs with electronic shut-off valves (SOV), running the a machine in winter worked best the next time by having a manual fuel SOV near the carb and letting the machine "run dry." Keeping the tank filled till the next use as well. Starting the next time with a dry carb bowl - of course opening the SOV and waiting a moment for fuel flow.
As for carb icing while the machine is in use, this will require a bit of effort/fabrication. As noted, tank heating ideas would have too much e-power draw.
Option one: There are heating elements for chainsaw handles out there. I have one saw and it comes in handy. It is switch operated and gets quite hot quickly. There is a small stater on the flywheel, so I do not believe much juice is needed. (AC source) I believe? This element comes in the form of a "tape" w/wire leads. Why? Ok, so I looked at an internet picture of the Predator 670 for reference. The cooling tin directs engine heat away from the intake side. I"ll call it a modern engine. Interesting fuel lines and such, so uhm, replacing part of the fuel line with copper or aluminum tubing as a heat sink and attaching the heating element to it would essentially provide you with a low e-draw fuel heater. A dash mounted switch and some trial and error R&D would offer a "fuel heater" and prevent icing. Mount a 5 0r 7.5 amp fuse in-line for good measure. A possible problem with too much heat in the fuel would be the an issue with vapor lock from vaporized fuel. There is no chance of electrical arcing as long as wires are insulated. Where to get? Amazon or the Stihl dealer. Humph ......
Option two: The carb "aluminum", bowl may be steel, is mounted via bolts through a rubber/plastic manifold. Heat from the heads being insulated from the carb. For various reasons, it is a good thing. Since aluminum is the least expensive yet best conductor of heat, even better than copper, using aluminum wire as a conductor of heat - taken from the cylinder head (wrapped inside the fins in some way avoiding too much air flow loss) and routed to the carb - wrapped around the carb body and/or float - insulating the wire if needed-when needed, would prove a heating element to the carb preventing the icing situation.
Option three: Like in option one where part of the rubber fuel line is replaced with metal tubing and utilizing option two's use of aluminum wire as the heat sink from the cylinder head(CH), a heating element is created warming fuel entering the carb. Yes, this needs a bit of R&D as well so as to get enough heat or avoid too much heat. Starting with a length of wire wrapped around the CH and while the engine is running, bare handed holding the wire and gauging how much CH wrap and length of wire will be needed and where insulation on the wire will be needed. As for the new section of metal fuel line, determining how much wire will be needed for the heating element is the first thing to solve. It'a ball-park - by hand or thermometer of your choice measurement. It may be a short, straight length or a small coiled length of tubing. To be determined by you, of course - avoiding vapor lock.
Ideas of where to get the tubing? I would try a big box home center or a very well stocked old time-y hardware store. The aluminum wire will be found there as well in the electrical supply section where off-the-roll 0 gauge or 2 gauge wire can be bought by the foot. Or a coil length of 8 or 10 gauge wire may be found where length rope is on the rack.
Insulation may be a bit trickier because it will need to be wrapped in close working quarters. Try the first aid section. Silk bandage tape (not paper tape) is a good insulator. I have used it to replace the covering on the armature of the starter/generator on older tractors. Or possibly exhaust wrap (expensive)? Insulation may even not be needed. (?)
I would think this "heating element" is best mounted aft of the fuel pump. Where is the fuel pump?
This is all simply an offering of ideas. The end result may look the child no one knows about because it's never let out of the house because it might scare the neighbors or could be hidden nicely and be the envy of who ever.
Keep the peace.