Avoid resurfacing with new. There is no way to make a permanent chemical bond, water will get in and it will crack out at any thickness that will not interfere with your use of doors and so forth. Don't let anyone tell you otherwise. This is regardless of climate. Don't believe me? Call your local cement supplier (call the company you see on the side of the mixing truck) and ask them.
To answer your specific questions:
Is it possible to resurface an exposed aggregate concrete patio?
And since you are not looking into how you do this yourself, I will encourage you to continue with the expectation that you will want to hire a professional for this work. Nasty chemicals and specialized equipment are involved that will easily damage adjacent materials and injure you.
They will grind your surface and wash with muriatic acid, very carefully masking everything around and up to the first floor ceiling plane - plants, siding, glass, everything should be diligently covered with lots of overlap and well taped/sealed seams.
This should be reasonably priced.
Is there a product that might work?
There is no one stop product for restoring both appearance and texture. You will need to mechanically refinish as well as chemically wash to restore eroded concrete and projected aggregate.
Now, do people overlay their patios all the time? Absolutely. This is how a tiled patio works. However, concrete needs the depth for the aggregate to provide the rigidity. You need 2" minimum for concrete, and if you do choose to overlay you will need to do extensive work to ensure the entire surface of your slab freely drains any water so that when water gets under your overlay, it wicks out to the edges. Hot weather causes vapor pressure expansion with trapped water (steam/cool cycles) as much as cold weather causes freeze expansion with trapped water (freeze/thaw cycles). There is no reasonable means to prep a fully cured concrete surface for an overlay under the minimum thickness. Under 2" the aggregate itself becomes the limiting factor. There is nothing to "bite" to with concrete.
To bring it back, my recommendation is to pay a professional to refinish it through grinding and chemical wash, or research doing this for yourself if you want to take on something advanced.