I'll second this. there is no problem with them per se, but having obvious ones will limit your options. Piercings can be a hazard, particularly in this day and age where you can be asked to wear a hard hat if there is some overhead work happening a mile from your location. It's not just "what if they got caught in a machine with you still attached" but also "what could they mess up if they fell out into a product." We don't accept watches, rings, earings, anything on the aero side of the business I work in. Don't underestimate the importance some companies will attach to health and safety - even if it means the job will take 3x longer and cost 8x more, they'll probably do it to avoid being sued.
Down in manufacturing and the shop floor where I work, tattoos are two a dozen. Come up to the design offices, and you'll be the odd one out. It's an industry with predominantly traditional values - there are companies out there who wont care, but for every one of those there will be 4 who do and may count it against you. You're not going to get "Piercings and Tattoos" as a reason on your rejection letter, but first impressions make a big deal in interviews and you can easily deflect the attention to your appearance rather than your ability which is what we're actually interested in. Interviews in my firm are generally done by senior management who represent the epitome of middle aged, conservative voting, whats-wrong-with-todays-youth type individuals. They're not going to discriminate because they can't by law, but that isn't going to stop them finding a legitimate reason not to consider you and weighting it heavily due to preconcieved ideas. Interview techniques and guides are all about presenting yourself in a way that doesn't draw out bias in the interviewers - and all too often in large companies, the person who interviews you will be nothing to do with the people you end up working for. No one said it was fair, it's just the real world.
So echo the above -go for it at uni, but ensure that you can revert to a professional appearance if you don't want to limit your options.