Swiss trip in December-- need help

hi all...

we are planning to go on 4 days trip to swiss mid december and plz find our itinerary
and kindly let me know if its practically possible..to cover all these places in 4 days..

1. Arriving on Friday 16.20 @ zurich.
Taking panaromic train to Zermatt which is 3.5 hours journey , overnite @ zermatt
Plz suggest cheap accomodations if any..

2 On saturday,. Early morning 8 take train to mountain top @ zermatt (Gornergrat)and come back to hotel
Take train to interlanken by 1 afternoon.

Reaching interlanken by 3 and starting for jangfraugh,schilthorn staying there till 6. and reach hotel for ovenite @ interlanken.

3. On sunday,Early morning by 7 leave interlanken and reach lucerne.
take Train @ 11 am to engelberg..
and even boat cruise @ lake thun or lake breinz,overnite @ lucerne

4. on monday, leave early morning to m t titlis and go bk to lucerne hotel.
Leave for zurich in the evening by 7 , overnite @ zurich

4.on tuesday, board the flight to dublin...back home..

Plz let me know if this plan would work out...or do I need to start early to cover all these places and lemme know if we need to look for accomodations closer to these places...and suggest few names of the hotels...

Many thanks..