Don't worry, i have figured it out.  I forgot the most basic method by adding
another increasing loop counter.

k=0

for (yr in 1982:2010) {
        temp <- ssta_sst[,,year_sst==yr & (month_sst>=6 & month_sst<=8)]
      k=k+1
        for (i in 1:360) {
                for (j in 1:180) {
                        ssta_winter[i,j,k] <- mean(temp[i,j,])
                }
        }      
}

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