Did the snowball earths kick-start complex life?
It is possible that the Makganyene glaciation played a role in the evolution of eukaryotes and the Marinoan glaciation in the achievement of multicellularity in (microscopic) animals. However, the fossil record provides no support for close correlations in time and causal links are entirely speculative.

In the case of the Makganyene glaciation, we are talking about the origin and adaptation of eukaryotic cells. With the Sturtian and Marinoan glaciations, the origin of macroscopic (visible to the naked eye) multicellular animals. The oldest body fossils believed to represent a eukaryotic organism, mainly on account of their size, is the cm-scale coiled form Grypania, which occurs in strata ~1.89 Ga in age in northern Michigan (USA). They are >300 Myr (million years) younger than the Makganyene glaciation ~2.22 Ga. Biomarkers (fossil organic molecules) attributed to eukaryotes are reported from strata nearly 2.7 Ga in age in Western Australia, but the phylogenetic specificity of the molecules has been questioned. There are far too few data to gain traction on a possible link between the Makganyene snowball earth and the origin of eukaryotic organisms.

As for early animals, it is useful to couch the question in terms of an evolutionary "tree", given the new light that molecular data are shedding on early animal phylogeny. Multicellularity in animals (multicellularity evolved much earlier in algae) is a trait common to calcisponges and eumetazoa, and presumably their last common ancestor. The genetic "tool-kit" for multicellularity (i.e., genes for inter-cell adhesion, signalling and differentiation) already exist in choanoflagellates, unicellular (occasionally colonial) protists that are "rooted" more deeply in the animal tree than the calcisponge-eumatzoa divergence. Molecular-clock analysis using a concatenation of different amino acid sequences, calibrated by known invertebrate branching-points across the Phanerozoic, places the calcisponge-eumetazoa divergence at roughly 650 Ma according to Kevin Peterson and coworkers at Dartmouth College (New Hampshire, USA). The next major divergence was the branching of the stem eumetazoa into cnidarians and bilaterians. The stem metazoa had evolved from eating bacteria to eating eukarya, a huge leap in the size of prey. The same molecular clock places the cnidaria-bilateria divergence at roughly 615 Ma, which is approximately coincident with an abrupt increase in the size, diversity, spiny morphology and turnover rate of fossil eukaryotic plankton, suggested by Peterson to be a response to predation. The absence of recognizeable body fossils or trace fossils at this time implies that animals were still microscopic.

The bilateria next divided into deuterostomes (echinoderms and hemichordates, which later gave rise to vertebrates including our own species) and protostomes. The last common ancestor to all bilateria (LCB) had a body plan that was differentated along a central axis and also top-to-bottom (dorsal-ventral). Molecular-clock analysis places it around 570 Ma, which is close to the first appearance of Ediacara, abundant soft-bodied macrofossils (up to 2 m in length), commonly frond-like, whose modular construction is unlike any extant animal. There is increasing doubt that they were animals at all, a view championed by Dolf Seilacher at the University of Tübingen (Germany) originally considered heretical. The last common protostome (LCP) branched into the ecdysozoa (animals that moult their exoskeletons, including arthropods and priapulids) and the lophotrochozoa (bivalves, annelids, platyhelminthes, etc.). Peterson's molecular-clock analysis places the LCP at roughly 550 Ma, which is not too far off the age of the oldest fossil lophotrochozoan, the 555-Ma stem-group mollusc Kimberella from Arctic Russia, described by Mikhail Fedonkin of the Paleontological Institute in Moscow (Russia). Evidence for locomotion on the sea-floor by the use of appendages is not seen in the trace-fossil record until the base of the Cambrian at 542 Ma, and the canonical Cambrian "explosion" of bilaterian skeletal diversity was delayed until 526-520 Ma (Tommotian and Atdabanian Stages of the Early Cambrian).

From the foregoing, it would seem that the achievement of multicellularity in (microscopic) animals would be the evolutionary step most closely associated in time with the 635-Ma (Marinoan) snowball earth. However, there is as yet no empirical support for this in the fossil record.