Here's my perspective after six months of owning an electric vehicle (Mustang Mach-e):
Instant torque, minimal "fuel" use while idling, regenerative braking and lower maintenance costs make electric vehicles perfect for postal use. It's also the same reason many police departments are trialing electric vehicles.
Heating/Cooling - running climate control has a negligible effect on battery life and range. I've heard reports of people camping in their car, running climate control all night and seeing only a 3-8% drop in range. Of course this was during temperate weather. Real world range will be less during winter in colder climates, a conservative drop of 20-30% of total range. Most of this is related to heating the battery and reduced battery efficiency in the cold, not climate control. There are strategies to reduce the weather-related drop in efficiency like pre-conditioning the battery before use that will mitigate this effect.
Charging infrastructure - Will require a massive investment in charging infrastructure. 40A chargers plugged into 240v lines at a minimum to charge in about 6 hours vs 14 hrs for a 120v plug in charger. However, this increased upfront cost will be offset by a massive decrease in maintenance costs - no oil changes, exhaust replacement, tune-ups, reduced frequency of brake maintenance (regenerative braking decreases wear on pads), etc. And the actual savings from replacing fuel cost with electrical cost.
Range - Most consumer electric vehicles offer total range of 300 miles, I'm assuming a purpose-built postal vehicle would have an even larger battery capacity.. Keeping the charge level between 20-90% to reduce battery degradation will shorten the range, as will winter weather in Northern locations. Even so, I would expect the percentages to be switched - electric vehicles meeting the needs of 90% of the routes.
Even ignoring the reduction in pollutants and environmental impact, it's a no-brainer.