Dickinson adopts her playful, little girl persona in this charming fantasy. For most readers, there are no hidden meanings, no symbols, just whimsy and pleasure in the beauty of sunrise and sunset.
If you've ever been up at dawn, you know that the sun's rays can appear as thin upward reaching streaks. She calls this phenomenon "ribbons"; if you took Core Studies 1, you may remember that Homer calls it "rosy fingers." The ribbon image is continued with the hills untying their bonnets, that is, the colors of dawn are getting brighter and the streaks more numerous. And dawn signals birds to start their day.
The description of sunset picks up an image of the dawn; the amethyst of dawn has darkened to purple. The stile (steps to climb over a fence) represents narrow clouds. The color of sunset as the children climb up is brighter than when they come down the other side of the stile, because the sun is lower and darkness is falling. The children are yellow (the color of the sun) climbing up. On the other side, a "grey" dominie or clergyman takes charge of the children. The reference to a dominie builds on the earlier steeple reference, both being religious images.
If you wish, you can read this poem symbolically. Sunrise and sunset are traditional symbols for birth and death, and Dickinson does use this symbolism in many poems. Ribbons, figuratively rays of light, may symbolize youth's vanity and innocence. Steeples symbolize religion or God. You may take this symbol even further; because steeples reach heavenward, they may be interpeted as humanity's yearning for heaven or union with God. In such a reading, the activity of the squirrels may stand for the frenetic pace of everyday activities. Boblinks symbolize dawn. The "dominie" could be the call of God or perhaps death, a caring, kindly figure.
I incline to Freud's opinion that sometimes a cigar is just a cigar, not a symbol for a penis (I'm not suggesting a Freudian reading of the steeple). What I mean by the cigar reference is, even in Emily Dickinson a sunrise and a sunset may just be that--the depiction of the sun rising and the sun setting. You can decide for yourself how to interpret this poem.