My car won't be driven during the winter, so from about November through March (5 months) it will sit idle. If I disconnect the negative terminal on the car battery when it's at full charge, should I expect the car to start in April when I reconnect it? The average winter high is usually around 30-40 degrees F.
I do what you are describing every winter in my RV and it starts fine in the spring, I have a marine disconnect on the negative terminal specifically for this purpose, and it's been fine sitting 4 to 5 months each winter since 2014.
Regular lead acid batteries do have a significant self discharge rate and by the time spring rolls around you are going to be sitting at something like a 60% state of charge, depending on your battery and the amount of power needed to start your vehicle there's a chance it won't have the juice to start.
Pulling the battery and trickle charging is definitely the safest option, but your fully charged battery will not die sitting out for the winter.
If you do only as you describe, you'll probably return to a completely dead and useless battery. According to the usbattery web site:
don’t expect to charge your batteries and come back in the spring expecting everything to be okay
The freezing point of a fully charged battery is listed as -80 °F and a fully discharged battery freezes at 20 °F. That may be colder than your expected temperatures, but it's not a good idea to risk it. Of course, a fully discharged battery is fully useless.
The article linked has other useful references, somewhat dry.
If you can add a battery tender (not a trickle charger) you will have a much stronger chance of keeping the battery healthy.
For those situations you can't provide electricity to your location, there are solar panel battery tenders to either connect directly to the battery or through the convenience outlet (formerly known as cigarette lighter outlet) or through the OBDII connector using an appropriate adapter, sometimes included in a kit.
It depends on the type of battery that you have. All batteries have what is called a self-discharge rate. It means that the battery loses certain percentage of charge just from sitting unconnected without being charged. The best answer would be to purchase a battery maintainer, such as the "battery tender" brand, or any other that is specifically designed to maintain your type of battery during storage. Alternatively, charging the battery every 2 months or so would be recommended.
As a rule of thumb, your standard, flooded-cell lead-acid battery self-discharges at a rate of 10% or more per month. Some of the "AGM" batteries can be as low as about 5% or more.
There are also several very expensive (approximately $300 +/-) "AGM" batteries that claim to use a "pure lead", and have other design features. Those types of batteries (examples are Northstar, Odyssey and X2Power) are usually substantially heavier than other types of batteries of an equivalent size, but they often offer more capacity and some of them have self-discharge rate lower as 1% per month, meaning that a fully charged battery can sit disconnected for 2 years, and still have approximately 80% of it's power available. I've used two of those three brands, and have had excellent experience with them.
Always fully charge your battery before storing for an extended time. Use a charger that is compatible with the type of battery you have, and start with the battery fully charged.
Hopefully this answer was helpful.