DA20 KATANA FLT CREW LANDS AT NOTAM CLOSED GRASS ARPT; AND ACFT SINKS INTO MUD.

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ON MAR/SUN/03; I WAS GIVING A PVT PLT A CHKOUT IN A DA20-C1 KATANA. AFTER FLYING AROUND THE PRACTICE AREA; I DECIDED TO HAVE HIM PRACTICE A SOFT FIELD LNDG AT SUMMIT ARPT. THE FIRST BAD DECISION I MADE WAS TELLING THE STUDENT TO PERFORM THE LNDG ON A RWY THAT WAS GRASS AFTER A LARGE SNOW MELT. THE SECOND MISTAKE WAS NOT CHKING NOTAMS AT SUMMIT TO SEE IF THE RWY WAS EVEN OPEN. THE RWY WAS CLOSED. NOT AWARE OF THE FACT; WE LANDED THE PLANE ON THE GRASS STRIP AND GOT THE PLANE STUCK IN THE MUD. THE PLANE HAD TO BE PUSHED OUT BY A GROUP OF PEOPLE; LESSONS LEARNED ARE -- CHK NOTAMS FOR ARPTS OF INTENDED LNDG; AND DON'T LAND ON GRASS RWYS THAT COULD BE WET AND MUDDY. THE PROB WAS CAUSED BY IGNORANCE ON MY PART; AS A FLT INSTRUCTOR; TO NOT ADEQUATELY CHK NOTAMS AND A LACK OF SITUATIONAL AWARENESS FOR RWY CONDITIONS. I NOW PLAN ON CHKING NOTAMS FOR EACH FLT AND STRESSING THE CHKING OF NOTAMS TO MY STUDENTS. AN ADDITIONAL WAY THIS COULD HAVE BEEN AVOIDED IS FOR A BROADCAST OF CLOSED RWYS OVER THE AWOS. AFTER THE PLANE WAS PULLED OUT OF THE MUD AND AN EXCELLENT SOFT FIELD TKOF PERFORMED; THE PLANE WAS RETURNED SAFELY BACK TO ZZZ WITH NO DAMAGE; JUST A LITTLE DIRTY.