Desperate to do the Transmongolian express... plan to be in Moscow on 1st March or would it be better to put it off until the 1st April or May if the weather is going to be so much better... therefore making the whole trip more fun.
Planning on traveling over land from Portsmouth England to Hanoi. then teach in bangkok.

March is the only month that I have not spent in Russia, mostly as friends always recommend against it.
March and April can be awful in Moscow because the weather can be freezing or the snow and ice melting. It is not predictable. Mid-Late April or early May is much better. Still not too many tourists but generally pleasant weather. If you travel earlier you will need lots of cold weather clothing as temperatures in Siberia and Mongolia will still be quite cold. See this chart: Temps along the TransMong route
Ruth