The link from Cervinia to Zermatt over the Theodul Pass is one of the iconic cross-border ski experiences in the Alps. A series of lifts takes you up to the Plateau Rosa, over the watershed, and down into the Zermatt ski area in Switzerland — a different country, a different language, much higher prices.
In good snow conditions and clear weather the round trip is a full day's skiing and entirely doable for a competent intermediate. The Italian terrain is easier; the Swiss runs back to Zermatt include some steeper, more interesting pitches. Bring euros, Swiss francs, and a passport — you cross an international border, though there is no check. Note that the link can close at short notice in bad weather, leaving you on the wrong side; check the forecast before committing.