we have been to mt titlis ( not the cliff walk? ) but the skywalk and ice cave etc and at various other 3000m high places in other nearby countries. we were at the der dachstein austria a few weeks ago and the dolimites italy before that (with lots of snow and ice caves etc at 3000m) we went out onto the snow and in the ice caves, suspended skywalks etc. we had jeans and wind jackets and just trail walking shoes/boots ( not real heavy walking boots) for clothing , layers are the go, anyway. ( not heavy coats)
the answer is, if the weather is good enough to go up and experience the mountain ( eg: if the visibility is good etc) then you are only really contending with cool outside temperature and snow on the ground.( your not there really for that long) so you can generally get away with a wind jacket and even joggers. unless you want to go hiking in the snow for many metres. or want to stay outside for a considerable time. if you need more than that , its probably not worth spending your money going there, eg: the weather is not good enough to see much anyway. and they all have a building at the top of the cable car, that you can stay in etc
each time we go up to these altitudes we see lots of tour groups ( generally from hot climates, eg: asia, india etc) wearing sandals and very thin street clothes and they are 'playing in the snow' that's what we call 'inappropriate clothing'. but they survive and have a great time, albeit a bit cool and perhaps wet one.
if you are doing a 'cliff walk', then ask the operator more about whats required. ( i am not sure on that point)
hope this helps.