The winds can gust fairly strong in Western Ireland at anytime of the year, so even though average temperatures in March may be around 50F, the wind can make it feel much colder. Wear a lot of layers and bring a really good waterproof jacket with a hood that can be tied tight (a hat or umbrella can be useless if it's raining and the wind is kicking up).
Not sure where you are planning to trek in the Galway area...The Burren, Connemara, Aran Islands? Yes, the terrain is fairly flat, but it's also pretty rocky on some of the trails and the ground can be muddy in March. You may want to bring 2 pairs of hiking/trail shoes in the event one pair gets too wet to put on the next day.
Italy will likely have less wind and a bit more sun, but the hiking trails in some parts are also rocky, so good trail shoes are in order and layers of clothes make the most sense.