It is definitely not a common idiomatic expression – it’s not something with a set meaning that we use. It actually probably doesn’t appear anywhere in French but in this comptine. So there is no set meaning to look for, it’s not going to be in any dictionary. Instead, we can look for an interpretation.

I found a French psychotherapist’s analysis here (in Au bonheur des comptines, by Marie-Claire Bruley). I quote:

“Le pouvoir de la comptine est d’accoucher de personnages hauts en couleurs et défiant eux aussi, par leur aspect physique ou par l’activité dans laquelle ils sont, le bon sens et la raison. […] Le côté incongru de ces formulettes tient en partie des inventions touchant à la perception de ce qui nous est de plus personnel, l’image du corps. Celle-ci constitue pour l’enfant l’enracinement même de son sentiment identitaire. C’est bien la façon dont il perçoit son propre corps qui l’assure de la réalité de la personne qu’il est. Quand ces petits textes […] décrivent la métamorphose d’une souris, verte de surcroît, en un escargot tout chaud, ils touchent à un rapport très intime que chacun entretient avec son propre corps. L’aspect fantastique qui s’en dégage alors naît d’un sentiment d’étrangeté déstabilisant le ressenti corporel habituel. Paradoxalement, ces comptines sont parmi les plus populaires et les mieux connues : ceci confirme l’hypothèse selon laquelle les enfants recherchent dans cette petite forme littéraire l’imagination la plus farfelue, les expériences les plus extrêmes. Il faut sans doute imaginer, jusque dans la démesure et dans l’absurde, pour s’enraciner avec profondeur et de façon paisible dans le sentiment que l’on est bien chez soi.“

In brief, the idea is that the child, imagining the most incongruous metamorphosis, builds a deep anchoring into his own body and being by realizing the distance between his actual experience and this extreme fantasy.

Of course, you need to have a serious psychological bent to accept this psycho-analytic interpretation. I’ve seen other interpretations, more “historical” but that didn’t sound quite as probable.

Edit: A translation of the cited passage by Luke for OP’s benefit:

The power of the nursery rhyme lies in producing colourful figures who also defy, by their physical description or the activities they carry out, both sense and reason. […] The incongruous aspect of this genre is partly the result of the inventions that touch on the perception of what is most personal for us: our body image. This is what constitutes the very root of the child’s sense of identity. It is very much a matter of the way in which he perceives his own body, which assures him of the reality of the person that he is. When these short texts […] describe the metamorphosis of a mouse — a green one, no less — into a “hot snail”, they touch on the very intimate relationship that everyone has with his own body. The fantastic aspect that thereby arises comes from a sense of incongruity that destabilizes the usual perception of the body. Paradoxically, these nursery rhymes are among the most popular and well-known; this confirms the hypothesis that children seek, in this minor literary form, the most far-fetched products of the imagination and the most extreme experiences. It is no doubt necessary to imagine, even to be taken into the outrageous and absurd, in order to deeply and peacefully root oneself in the feeling that one is comfortable in one’s own skin [or that one is at home].

It’s just a seemingly-silly whimsical nursery rhyme, yet it has a profound effect on babies and toddlers as it prepares them to phonemic awareness. Thus the meaning is not really important, it is the rhythmic sound of rimes that matters. However, for older kids (and adults too!), the nursery rhyme whimsy of the “souris verte” is also designed to make the spirit light-hearted, to take it away from dullness or worry and bring it “outside the box”. The psychotherapist’s analysis isn’t too far off…either.

There is an explanation understood through alchemy. See the work of the French alchemist Patrick Burensteinas
https://www.youtube.com/watch?v=5Sr4mPRst_g
He uses puns in what he calls la langue des oiseaux. For example, he associates the green color to the word "envers" (en vert / in green) meaning the reverse. The suggestion is to enter the spirit world, the other side of the material realm .

Also watch this more complete explanation at 5:06 minutes
https://www.youtube.com/watch?v=pfp6124ovb0

I personally work with dream incubation and my interpretations are Jungian. I have a different explanation for the word queue. My understanding is that a queue (tail) is the kundalini energy which in this case is outside the body thus not integrated to the Higher Self.