The series of molecular signals initiated by binding of a Wnt protein to a frizzled family receptor on the surface of the target cell, followed by propagation of the signal via beta-catenin, and ending with a change in transcription of target genes. In this pathway, the activated receptor signals via downstream effectors that result in the inhibition of beta-catenin phosphorylation, thereby preventing degradation of beta-catenin and contributing to cardiac muscle cell fate commitment. Stabilized beta-catenin can then accumulate and travel to the nucleus to trigger changes in transcription of target genes.