I work for one of these startups, Beta.
We are focusing on a slightly different market than the other entrants; we're focusing initially on cargo rather than passenger transit. One initial customer is United Therapeutics, for transporting organ transplants and artificial organs to hospitals. Another is UPS, for getting air freight from airports to distribution centers; cutting out the truck trip can save a ton of time there. We are also making a passenger variant, but since the regulatory and NIMBY concerns for the passenger air taxi market present a lot of risk, we're not betting solely on that market like a lot of the other companies are.
This helps with a lot of the concerns raised in this thread. In fact, another one that I'm not sure has been brought up is vertiport design and siting concerns; right now standards on vertiports are still a work in progress, and there are questions about whether it will be feasible to get them installed, because even with vertical takeoff and landing you generally need to keep approach angles of about 15° clear, which means once a vertiport is installed you need to limit the heights of any surrounding buildings to keep the approach clear.
To address a few of your other concerns: we're located in northern Vermont, we know cold weather. Actually, for our use case hot weather tends to be more of a concern; batteries and motors heat up when used, especially in the very high power vertical lift phase, so our limitations there tend to be thermal and cold air provides better cooling.
Our charging stations also include air for cooling and warming the batteries; so you should be able to avoid the issues with batteries being cold on startup with our air system.
All aircraft have limitations on weather that they can be flown in; crosswind limits for takeoff and landing, etc. As very lightweight aircraft, with high lift/drag, these will be somewhat lower than the limits for your big jumbo jets, but will be high enough to be useful in a lot of weather. All aircraft have requirements for design and testing for HIRF (high intensity radiated field/lightning), so these will all be certified to the same standard there. Aircraft can optionally be certified for flight into known icing conditions (FIKI); I believe our plan is to have the capability, but as an optional add on, as it requires a number of heating elements which add weight and complexity. But overall, the weather concerns shouldn't be too much different than for other small aircraft.
As far as safety goes, that's obviously a concern in any aircraft. One advantage of electric aircraft is that electric propulsion systems are far mechanically simpler, with far fewer moving and wearing parts. The only real wear item of concern are the main bearings on the motors, and the landing gear. So maintenance intervals can be much longer than with ICE aircraft, and I expect reliability to be considerably higher. Additionally, electric motors can be much smaller and lighter, and thus can be made redundant. Each propeller on our aircraft will be driven by multiple independent motors (probably can't say the exact configuration at the moment), so that motor failures can be tolerated without catastrophic consequences.