Note: In this part of Italy, most people speak German, hence most objects have a German and an Italian name. Where I give both, the German name is the first.
The Madritschspitze / Cima Madriccio lies in the eastern part of the Ortler Group and offers great views on some of the famous mountains all around, especially the big three, Ortler, Monte Zebru and Gran Zebru, but also the Cevedale.
The Madritschspitze is the first peak on the ridge connecting the Madritschjoch / Passo del Madriccio (3123 m) to the Eisseejoch / Passo del Lago Gelato (3139 m). The other peaks on the ridge are the Butzenspitze / Cima Pozzo (46.4862, 10.6230) (3300 m) and the Eisseespitze / Punta del Lago Gelato (46.4805, 10.6087) (3230 m).
East of the peak lies the Madritschtal / Valle Maddricio, to the south east the Butzental / Valle del Pozzo, to the west lies the Solden ski area.
The Schaubachhütte / Rifugio Città di Milano (2581 m) and is the highest point in the route to the Zufallhutte / Rifugio Nino Corsi (2265 m). This route is popular for hikers and mountainbikers alike. If there isn't too much snow, the hike to the pass from the Schaubachhütte takes about 1.5 hours, from the Zufallhütte about 3.
Just north of the pass lies the Punta Beltovo / Schöntaufspitze.
The Eisseejoch lies about 2 km south by south east from the Schaubachhütte and is on of the glacier route from the Schaubachütte to the Cassati refuge, from where many people climb the Cevedale. In fact, quite a lot of people climb Cevedale directly from the Schaubachhütte, and considering the prices at the Casatihütte, I cannot blame them. Note that this is a glacier route, with lots of crevasses!
Getting ThereThe best access is either from the small town of Sulden / Solda, or from the Martell valley to the east. See Punta Beltovo / Schöntaufspitze for more information.
The Easiest RouteThe easiest route is hiking up from the Zufallhütte through the Martell valley and the Butzental. Count on 3-4 hours to the summit.
From the hut, follow a good path into the Martell valley, initially going south, but soon it turns westward. Ignore the turnoff to the left (or south) that descends to the river and the Martellerhütte and continu along the path up into the valley, ascending gradually. The path doesn't follow the valley floor, but stays on the slopes, and very gradually turns towards the north west.
By now you're into the Butzental, which ends at the ridge connecting the Butzenspitze on the left and the Madritschspitze on the right.
We followed this route on the descent.
North RidgeThe approach from the north, from the Madritschjoch, is a nice scramble along the north ridge leading to the summit, UIAA grade I-II.
The ridge is quite exposed at some places. Route finding is easy, just follow the ridge. You can see the summit cross on and off while on the ridge, but you'll have to pass quite a few false summits before you finally see it up close. We took a leasurely two hours, but it shouldn't be too hard to climb it within an hour.
Other RoutesThere are two more easy routes worth mentioning, though I have no personal experience with these.
AccommodationWild camping is not allowed, but there are plenty of alpine huts nearby. In winter, Sulden is a ski town, with lots of accommodation options. In summer, it is a pleasent town and not so busy anymore, so it's easy to find a place to stay.
The two most relevant huts are
Before moving to the Schaubachhütte, we stayed at Garni Ortlerhof and I can certainly recommend that.