Context
In Spanish 1 & 2 I was taught expressions such as tener frío, and tener sueño. Some of the English phrases to be + adj are tener + noun in Spanish.
I have noticed that many English adjectives ending in -y that have a nominal complement are used in such expressions: thirsty (thirst), hungry (hunger), sleepy (sleep), happy (happiness), gloomy/glum (gloom, sadness) -- with the exception of hurriedness (hurry).
I understand that Latin does not have a verb meaning "to have," so I assume that tener carries with it a meaning slightly different than what an English speaker would expect.
Question
What extra meaning, if any, does the construction carry by using tener instead of ser or estar? (N.B. I know the uses of ser and estar and when to use each.)