It seems that MICE does not have a "predict" function which allows to use a fitted
mids object to predict the missing values in test data set. I can certainly combine the training and test set together, do an imputation, and then split them as before. But I think in this way the imputation model also uses information from test set, which forfeited the purpose of setting up a test set in the first place.
I wonder if there is a more elegant way of doing imputation for test set using MICE (or other packages). I see that the method described in here https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm#missing1 are promising. But does it mean that I have to embed a Random Forrest in my model only for imputation?