For those not familiar with the sound, here's the description from the Peanuts Animation and Video List:

Q: How were the adult's "mwa-mwa-mwa" voices made?

A: With a trombone. Leonardo Morán of Bill Melendez Productions says:

Composer John Scott Trotter directed his trombonist to 'enunciate' the teacher's dialog as though it were a trombone riff. Trotter did a great job... he would read the teacher's line, e.g., 'Linus, where's your homework?' then direct the trombonist to repeat Trotter's inflection through his instrument.