To hold some one close to you in an embrace, cuddle, snuggle and hug combined. The period of shnugglebugging can last from 1 second up to... until your bones and muscles become stiff shnugglebugging in one position for an extended period of time.
can also be used as a noun where by the special person you are shnugglebugging is referred to as the shnugglebug and you are the shungglebugger.