How would one impute missing values for a Discrete variable?
It depends, if you have the distribution of that feature, you can take the marginal distribution over that feature which its interpretation is to use the expected value of that feature. If you don't have the distribution you can take the mean of the sample in hand of those samples which have value for that feature and add the mean for those which don't have. Another solution is to separate the data of each class and find the mean of the feature of those data samples having the value and putting the mean for each entry of the corresponding class which does not have value in that entry.