NOT ANY MORE, Switzerland is now a Shenghen State, meaning one need to obtain Shenghen Visa to even visit there even if you have resident visa for UK.
for the Italian visa holder not the passport holder, I assume same Shenghen visa rules applies, if you have visitor or shenghen resident visa without any country restrictions you can visit as there will be no visa requirement as both of these countries have signed to shenghen visa agreement.
best would be check local italian embassy of switzerland website for more info.