After the catastrophic issues of the Earth's spin suddenly stopping have settled, then yes, one side would become desert hot and the other would be an ice age. Life would only survive between the two sides, to varying degrees, based off how far away you were from the border.

Think about summer and winter as it is now, the extremes of "seasons" that earth currently has is purely based off how far away you are from the equator during specific times of the year. The equator is always warm because it's exposed to the sun on average more than any other part of the world. The further north or south you go the temperature varies in magnitudes higher. All because the Earth's tilt let's you see less or more sunlight/heat radiation in a day.