I live in rainy SW Florida, and over the last 8-10 years have seen and talked to owners of three ebikes disabled due to water intrusion.
Yes, you need to take precautions.
If you have a throttle, you need a temporary cover as water intrusion is common here, and will disable the bike. No permanent damage, but no power till you dry it out. Have experienced this twice. Strip of small plastic grocery bag makes a good, temporary, disposable cover. Note that powered accessories on throttle body can make this far worse, I avoided those.
Controller ideally fully potted, otherwise drip loops in wires and consider adding drainage holes. Remember that everything you do to keep water OUT, will also act to keep water IN.
Most common serious problem area is charging port for battery. Often recessed allowing water to pool, covers provided not really adequate. Water intrusion can severely damage battery. Additional exterior cover which will also help hold the provided cover firmly in place recommended. Not having contacts at the bottom of a vertical channel also a good idea.
My bike has been strapped to the front of a bus doing 50mph thru monsoon-level rains for over 30 minutes, several times for shorter times, no problems. Throttle cover, drip loops, potted controller, waterproof sealed cover for charging port, waterproof battery housing.
After putting the system all together i can see the wiring connections are sealed quite well. I did use some dielectric grease on the battery contacts and connection. Probably only a matter of time before i get caught out in a downpour. Will habe to cut some strips of plastic bag to protect the throttle as Nelson suggested. The rubber cover on my batterie's charge port fits tight and seems adequate.
The rubber cover on the batteries charge port was the part that failed on two of the three disabled ebikes I talked to owners on. The third had a vertical mount battery. I suspect those are relatively watertight with the battery in place, but when the battery is removed, not so much.
On the rubber cover, it is fairly easy to bump one out of the way, also they degrade over time and can get stiff, particularly when exposed to strong sun. It only needs to be partially on ONCE, when you get rained on.
My charge connector goes into a seperate, waterproof, vertical sleeve.
All wires run thru old 700c thin inner tubes used as conduit. Makes a perfect seal on the plastic nut cover over the hole in the axle.