Why does my 6 year old start aggressively and randomly nipping at visitor's feet?

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How old is she and what breed/mix? Some breeds, especially herding breeds, will develop this tendency to satisfy their herding instincts, which may explain why she's not really trying to hurt anyone (if I interpreted what you wrote correctly). The timing may be due to her age, especially if she's a younger dog (less than 2 or 3 years). It could also be a fear response - maybe she doesn't like the sound certain shoes make (especially if her behavior is specific to certain kinds of shoes). Make sure she gets plenty of exercise. Bad habits have many causes, and one of the most common is pent up energy and resulting frustration. Make sure she has some toys she likes so she's not bored (maybe shoes are becoming really entertaining for her). If these interventions don't help, try simply blocking her from being able to do the behavior until she gets used to not doing it again and realizes you're not going to let her do it.

Hmm. Have there been any changes or upheavals? Can you think of any differences in her life this past year? How long have you had her? If you haven't had her since she was a young puppy, what do you know about her life with the previous owner? What is an "average day-in-the-life" like for her?

My old teacup yorkie used to do the same! When someone enters the house they would not bother. But once someone is in the house, walking around and near me (hugging, or too close) he would start to nip at their feet. He was tiny but very protective of me. So my opinion, I think that's exactly what it is. Protecting their owner :)

Could be a herding behavior; the quick nip-and-dart is a common tactic of herding dogs. Those innate behaviors are easy to fall back on when a dog is bored, frustrated or stressed. It could just be a fun game for her that she's picked up recently. A smart, high energy dog will give herself things to do if she isn't provided with enough stimulation in her day to day life, and you may not think her self-appointed jobs are very useful or fun. Channel her energy in other ways with lots of exercise and mental stimulation.

Also, as Jean suggested, restrict her access to guests so she can't practice the unwanted behavior until she's learned how you want her to behave around company.