Where the snow song spell effect to move with the caster, the spell would likely have header entries like those of the Sor / Wiz level 6 spell antimagic field (conj) (PH 200) and be, instead, an emanation: "An emanation spell works like an exploded spell, except that the effect continues to radiate from the point of origin for the duration of the spell" ((PH 175). the snow song spell effect do not an emanation and has no special rules saying otherwise, so its effect stays where it was placed like most other non-emanation effects that don't otherwise specify.
In other words, the level 6 bard spell snow song (e VOC) (Frostburn 105) creates a stationary area. Although the spell area is measured from the caster, like the similar 1st level Sor / Wiz obscuring mist (conj) (Player Manual 258) and the extremely similar level 6 bard spell funeral song (e VOC) (Spellbook 65), the snow song the spell effect is stationary.
To be clear, the snow song The description of the spell begins with the following:
When you cast the spell, you must designate all creatures in the area as allies or enemies. ((Fr 105)
And it ends with this:
These advantages remain in place as long as the spell persists and as long as the target remains in the area of the spell. Yes a creature leaves the spell area, all effects end for this creature until it returns to the snow songThe area of. ((ibid.)
(Emphasizes mine.) It goes without saying that spellcasters generally refer to themselves as allies and tend to want to stay in that area. (Its stillness also explains why this guide lists the snow song spell as a medium spell choice for the typical bard.)
Note: While the mist the description of the spell says that its effect "is stationary once created", this reader assumes that this recall is due to the status of the spell as a 1st level spell, its clarification just there so that new players to the spell do not ; do not need to consult these rules. Because of its Range the entry of a DM can decide that a caster can assign spells like obscuring mist and snow song with the Complete Arcane feat Persistent Spell (81) (see, for example, here; in such cases, the effects would remain for 24 hours where they were launched, completely still.