Same reaction: your plan involves a lot of travel.
The Riviera, Italian or French, can be very quiet in February, and is not at its best - March or April would be better.
I would focus on winter activites in Switzerland, if you can afford it. If you still want a bit of "italian flair", instead of Portofino, you could spend 2 days in lake Como before flying out of Milan. Lake Como is also not at its best in Feb, but it is close to St Moritz, so at least you do not waste too much time getting there.
I would stay in Luzern rather than in Zürich.
And you could easily spend 5 days in the St Moritz area. Unless you can afford the best hotels there, which have a lot of "old world charm" (e.g. Suvretta House or Badrutt Palace Hotel), I find St Moritz itself to be a bit charmless, despite the beautiful location.
Instead, in winter I would recommend:
- Pontresina.
- Sils in Engadin, small place, at the foot of the Corvatsch and between 2 frozen lakes (well, usually frozen)
- Celerina, next to St. Moritz, with less concrete. In summer, I would have said Samedan instead, but Celerina is more convenient for winter activities
- A bit further afield, Bergün, a very cute village in the Albula valley with an iconic sledding trail.
EDIT: I forgot to add, and this is important: check that your insurance policy covers sledding/tobogganing. The risk of injury is high. Specialized winter sports insurance should cover it, but double-check. And use a ski helmet.