I will be away from winter through early spring, approximately 4 months. My 2014 Sierra truck will be in my garage. Should I remove the battery completely or just disconnect and tape up the negative terminal. We live in Belleville, Ontario area.
I'd just disconnect the negative, personally.
I'd also recommend having a look at some of the questions and answers on here about storing vehicles for a long time:
As these may give you other useful advice - for example, jacking it up so you don't get flat spots on the tyres.
I would put the battery, with it still connected to the vehicle, on a trickle charger.
This is because you will lose all the computer stored settings, and that may be a problem.
I did this, but for a shorter period of time, with a small (up to 10amps) charger on a time switch. I kept it down to 2 hours a day and it worked fine.
Are you trying to keep your battery from discharging? Are you worried about a parasitic drain? Or are you worried about temperature?
A better choice for long-term storage might be a battery tender. That will keep the battery up to the right level without overcharging.
Having lived in North Dakota, my experience was that the extreme low temperatures in the timeframe you mention it is best to remove from the vehicle and put inside at room temp. Extremely low temperatures are not good for a battery, and neither is not running it frequently. Both those things together will impact your batteries overall lifespan.
The freezing point of the battery electrolyte becomes lower the more fully the battery is charged (I've found many different numbers for freezing point of a fully charged battery, and you can too), and even disconnected the battery will self-discharge (increasing the risk of freezing). I'd go with a battery tender myself (which also avoids the loss of volatile memory).
Definitely bring the battery inside the house for the winter period. It helps the battery to stay warm. Frigid cold as well as hot summer days, are not not helpful for a car battery. Speaking of very cold winter days, to start the car even easier in the morning, bring the battery at night inside the house, it will be more powerful in the morning if the battery is kept warm.
I would take it out because the longer it sits the battery will loose its charge. Don't worry about it loosing stored computer settings their store on a memory chip like ram on a computer