Training set does not have missing values, but test set does. How to handle? For a modeling challenge, I was given a training and test set separately. Since my training set did not have a substantial number of missing records, I omitted all rows with NA's. And trained my model on a complete data set.
However, my test data set also contains NA's. I don't have the luxury to remove any test data set rows as I need to generate predictions for each row. How should I approach this problem? Would it make sense to use imputation methods (e.g., MICE) on just the test data set, even though I didn't need to impute anything in the training data set?

Yes, that would make sense.
First, note that you can omit rows with missing data during training provided you are sure that your data is missing completely at random (MCAR). Otherwise, you should apply some imputation technique during training. And even if you think that the number of observations you would omit is not relevant, it wouldn't hurt to also apply imputation for comparison of results.
But, independent of whether you used imputation in training, if you want to apply it to new data with missing values, you can apply imputation on the independent variables, and mice is a good choice.
