Do you have any more context? From this, I'd guess it either means that the greenery is blowing about in the wind, or it just means that the greenery is abounding or overflowing. In British English, "tossing" has a not-very-polite meaning, something like "darned" but ruder (but not so rude as the f-word).
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Avangi
Hey, guys! It wouldn't have anything to do with the makin's of a tossed salad, would it??
("tossing greenery" = green vegetables to be tossed in a tossed green salad?)