This is the 2255th most frequent Swedish word.
väldigt
"Väldigt" means "very" or "extremely" in English.
Here, 'väldigt' modifies the adjective 'kallt', intensifying its degree to imply a higher level of coldness.
Det är väldigt kallt ute idag.
It is very cold outside today.
In this case, 'väldigt' modifies the adjective 'intresserad', emphasizing the subject's strong interest in music.
Han är väldigt intresserad av musik.
He is very interested in music.
The word 'väldigt' strengthens the positive connotation of 'trevlig', indicating the extent of enjoyment experienced during the evening.