You did not really specify where exactly you want to go, but since you mentioned Jungfrau region, I assume that you're talking about Jungfraujoch.
As Kathryn Hill already mentioned, it can get very cold up there. But this is not only the case in winter. Since it is around 3500 meters above sea level, it is cold year round up there. Even now in autumn, it can get as low as -20° C. And even in the highest summer season, the temperature might be around 0°C. So you should really be prepared for cold weather during the whole year.
I would recommend that you particularly focus on wearing warm shoes that are water-proofed so that you won't get wet socks. Nothing is nastier than wet-socks when it's cold out there. Furthermore, bring a warm cap with you and I'm sure you won't regret if you also bring gloves with you. I personally would also wear a warm jacket, especially one that stops the wind. If it's cold and windy, you will easily suffer from wind chill. Trousers are not so important if you don't plan to lie or sit in the snow. In this case a normal jeans (if you prefer with long underwear as Kathryn Hill mentioned) is enough. Otherwise, I would recommend a waterproofed trouser.
Additionally, you should not forget to wear sunglasses. If the weather is nice, the sun is very bright and since on Jungfraujoch, there is snow all year round, the sunlight will be reflected heavily. For the same reason, also make sure to bring your sunscreen with you.
If you plan to walk in the snow, you could also borrow gaiters to prevent snow getting in your shoes.
Concerning your medical question: There are medical hints on the Jungfraujoch homepage. The biggest danger is altitude sickness. Altitude sickness is caused by the decreasing air pressure and oxygen level in higher altitudes. However, normally, the first symptoms of altitude sickness will not be visible before 6-12 hours, so, normally, this shouldn't be a problem in your case. However, I would recommend to read the medical hints to be on the safe side.