why do people get a nose bleed for no reason at all?

Onset of nose bleed can be caused by so many factors; one reason I know is the membranes can be so dry it is a way of lubricated the nostrils but not in a healthy manner. It can be caused by so many other types of conditions as the eyes, ears and throat are connected together which may be another leading problem stemming form there and well the bleeding out of the nose is the only way out.

probably it's because of heat... can we actually get nosebleeds when it's cold?

There are a lot of unseen causes for nosebleeds. It could be the hot weather, the dryness in the air or lack of humidity, or even the coldness. Nosebleeds are caused by ruptures in the tiny, delicate veins inside of your nose.

One of the reasons people get nosebleeds in the winter is because the outside air is generally much dryer during the winter. In addition, everyone is running their heating systems, and most heat nowadays is very dry (as opposed to the old radiator/hot water heating systems of years ago). All of this dry air dries up the protective mucous membranes in your nostrils, and the tiny veins & capillaries can therefore burst much more easily. Running a hot-air humidifier in your bedroom at night is one way to help prevent nosebleeds, dry skin, chapped lips, brittle hair, etc.--all which can happen during the cold, dry winter months.