Energy flow is driven by differences in energy.
- Rocks fall from high potential energy to low potential energy
- Electricity flows between negative and positive
- Heat flows from warm places to cold places
- Wind blows from high pressure to low pressure
If the Arctic warms faster than the equator, that reduces the temperature gradient and reduces the ability for heat to flow. It means fewer storms, fewer cold fronts, warmer air, etc. Consider Venus. It has a uniform hot temperature, and essentially no weather.
People who claim that a warming Arctic produces more cold air and storms, are scientific imbeciles. Enter Obama’s science adviser. We are truly dealing with the stupidest people who ever walked the planet.