Roze is the name of the color: roze = pink. When the word was borrowed from French, it was spelled rose, and some Dutch speakers (Nederlandssprekenden) still use that spelling (rose), but it is no longer considered correct.
Roos is used as the name of the plant (de roos), but not as the name of the color (roze) nor as a color adjective (bijv., het huis: een roze huis). The color in all contexts should be spelled 'roze.'
You will also encounter Roos as a last name (achternaam) or as a girl's name (meisjesnaam).
Roos is also used for bullseye: in de roos schieten (score a bullseye) or more figuratively, to be on target (bijv., dat was midden in de roos), or for dandruff (hoofdroos), among other things.
I am not a native Dutch speaker, but here is my take.
Many sentences don't seem to make sense without context, but make perfect sense in context.
'My favourite color' would be 'mijn lievelingskleur' or 'mijn favoriete kleur.'
If someone were to say, "Vertel me je lievelingskleur," you might respond, "Mijn kleur is roze," but then 'lievelingskleur' would be understood from the context.
This sentence is literal: Haar kleur is roze. Her color is pink. 'Haar' also means 'hair,' so in some contexts it can also mean: Hair color is pink. 'Haar' can also refer to a feminine noun: Its color is pink; it is pink.
Here are a couple of examples I found online:
"Rafi de giraf is een superzacht knuffeldier. Haar kleur is roze."
Rafi the giraffe is a super-soft stuffed animal. Her color is pink. / She is pink.
Haar kleur is roze. (Zij is roze.)
"Karin werd geboren op een donderdag, 10 mei 1979, onder het Chinese teken van de geit. Geiten zijn creatief en romantisch. Haar sterrenbeeld is Stier. Een stier is bedaard. Haar geboorte bloem is de klaver. Haar geboorte steen is de smaragd. Haar kleur is roze."
Karin was born on a Thursday, May 10, 1979, under the Chinese sign of the goat. Goats are creative and romantic. Her constellation (or Zodiac sign) is Taurus (the bull). A bull is calm and collected. Her birth flower is the clover. Her birthstone is the emerald. Her (birth) color is pink.
Haar kleur is roze. (Roze is haar geboortekleur.)