Is it
Edelweiss?
My sisters like it warmer,
The flowers prefer warmer climate
I survive in the cold.
But the edelweiss grows in the cold mountains
The others are low.
The other flowers are low-er, i.e. in the planes
But high I grow.
But the edelweiss grows high in the mountain
Yet I am not tall.
Though it is a fairly small flower
I am small, noble and white.
It is, indeed, the plant is small and in German edel-weiss means noble-white
Many seek me -
It is a popular thing to search for in the mountains
A few see me, a few die.
Some see it, unfortunately the mountains could be dangerous
Some strongly protect me,
It is a protected plant in many countries
Others sing songs in my name.
There are popular songs in its name.