Is there any known Bayesian, ML or MDL interpretation of cross-validation? Can I interpret cross validation as performing the right update on a specifically crafted prior?
Cross validation is aimed at unbiased estimation of the risk (aka Test Error, or Prediction Error). In the case your loss function, is minus the (generative) log likelihood, then cross validation will return the expected log likelihood of your model. The same holds if your loss function has a Bayesian motivation.
MDL is also aimed at unbiased estimation of the risk. It is thus an analytic approach to what CV does computationally.
See Section 7.2 in Elements of Statistical Learning.