Passing a std::array of unknown size to a function

Is there a simple way to make this work, as one would with plain C-style arrays?

No. You really cannot do that unless you make your function a function template (or use another sort of container, like an std::vector, as suggested in the comments to the question):

template<std::size_t SIZE>
void mulArray(std::array<int, SIZE>& arr, const int multiplier) {
    for(auto& e : arr) {
        e *= multiplier;
    }
}

Here is a live example.