To stay at a mountain station and do day tours is popular and not particularly complicated. Most equipment you need is rentable on site and the clothing you need is probably with your outdoor clothing at home.
Clothing
If you avoid cotton nearest to the body, since it cools when wet, and have windproof outer clothing, the winter day out will a nice experience. Use sunscreen with a high factor and sunglasses, even if the sun is not breaking through the clouds. Here is an example of how you can dress:
• Underwear in wool/synthetic
• Thin sock in wool/synthetic
• Wool socks
• Shell jacket or anorak with hood
• Ski pants, unlined
• Sweater or shirt
• Mitten windproof, preferably with removable liner or inner mitten in wool
• Hat
• Sunglasses and ski goggles
In the backpack
A backpack that holds 40 litres is plenty for a day tour. It holds only what you need for it to be comfortable and safe out there; something to eat, sit on, rest garment, wind sack and shovel. Even if the weather is nice, a wind sack can be useful during a break if it is windy. The small, versatile shovel is just as good at digging a rest stand as digging a bivouac. Not to mention what entertainment it is for the kids.
• Extra garment; down jacket or thick sweater, wind pant
• Coffee/food and vacuum bottle
• Sitting pad/sleeping pad
• Toilet paper
• Wind sack and shovel (one for 2-3 people – can be rented)
• First aid and sunscreen