That's often very early in the morning, but varies according to the street. (One with lots of bars and nightclubs might allow deliveries during the day.)
For example, Copenhagen's main pedestrian streets are restricted to people on foot at all times, except residents at any time, and delivery vehicles between 04:00 and 11:00.
Basically this problem is absolutely solvable if you actually want to
Can you imagine working a job like this when it's cold outside and you potentially had ice the night before? And to solve this problem you'd basically reinvent the car/truck.
In icy conditions, it's likely safer for most citizens to have delivery done by bicycle. They're slower and lower mass compared to a van.
In cold, the delivery person can just add layers. And, they'll be moving more, so in all likelihood, the additional layers required is minimal. It's not like a UPS van is super warm inside - not with the driver constantly opening the doors and hopping in/out.
It simply boils down to priorities. Do we want cheap/easy delivery to merchants or do we want safe pedestrian and bicycle zones for customers. Or, is there a magical balance point in the middle?
Also I highly doubt these tiny bicycle tires can handle a pallet of bottled water or beers. They will just get crushed.
By the way, why is it so important that deliveries get done within an hour?
Second in line are delivery and post vehicles regularly blocking the cycle lanes.