Hi Michael, and welcome to MySwissAlps!
>> My wife and I plan and spending our 1st anniversary visiting Zurich for a day or two followed by some time spent in St. Moritz for some snow activities.
If you don't have a specific reason for staying in Zürich, I would suggest heading straight for St Moritz and spending most of your time there. However, if you happen to be travelling between early April and late June, or between mid-October and mid-December, mountain transport in the St Moritz area will be closed for maintenance, for periods varying from 4 to 6 weeks, and I would not recommend spending that time in St Moritz.
>> Part of the trip is seeing the countryside but we are limited by our time. What is the most scenic option by rail from Zurich to St. Moritz, and if there are drawbacks to it what are they?
The most scenic option would be to follow a small part of the Gotthard Panorama route, followed by a substantial part of the Glacier Express route, i.e. Zürich > Erstfeld > Göschenen > Andermatt > Disentis/Mustér > Reichenau-Tamins > St Moritz. This would take 6 hours 49 minutes.
Two shorter, less scenic routes are (in the order in which I personally prefer for scenery):
Zürich > Landquart > St Moritz (about 3 hours)
For a description of this trip (in the reverse direction, with photos) see my post of Feb 28, 2017 - 4:36 AM on the following page:
Zürich > Chur > St Moritz (3 hours 21 minutes)
The stretch from Chur to St Moritz is very scenic.
If you could provide the exact dates of your trip, and what you mean by "snow activities", we could better tailor our suggestions and advice :-)