This is a norm that has changed. Not long ago, simultaneous submissions were frowned upon. Now they are largely expected. However, publishing tends to be an old-fashioned industry. There are still hold-outs that have different expectations, so make sure you check the submission guidelines for each publisher.
I would recommend, however, that you query first, rather than submit. This means sending a letter describing your manuscript, and waiting for it to be requested before sending it. There are several reasons for this, including that you are free to query as many publishers and/or agents as you want at any time. You are also much more likely to have an unsolicited query read than an unsolicited manuscript reviewed. You can also query in bulk, and/or tweak your query over time.
Many agents and publishers ask for the entire text of the manuscript to be included in the query for picture books, since those manuscripts tend to be very short (only a few pages of text). This still does not count as a "submission," per se, in terms of simultaneous submissions. If you are lucky enough to get multiple requests for your manuscript, each of those counts as a submission. It is appropriate at that point to ask whether simultaneous submissions are allowed, and to consider whether you do WANT to submit simultaneously or not (for instance, you might want to wait for a response from your first choice publisher before submitting to your second choice).