Hmmm, gosh, Natalya. I enlarged the picture as much as it would enlarge and I could not identify leaves with rust spores (orange spots). Of course, sometimes the lesions are small enough so they do not photograph well. Below is a link with a picture/example so you can compare it to the leaves in your plant.
I did notice some stems that winter zapped. Those can be pruned all the way down if they do not leaf out by the end of this month.
Typically but not always, rust pustules appear on the undersides of the hydrangea leaves but, in heavily infected hydrangeas, the upper surface of leaves may turn brown or yellow and drop prematurely. Let me know if that is what you are seeing. If not, can you please take a close up picture of the leaf lesions?
Note that this disease is usually seen near the end of the growing season, not at the beginning, and it rarely kills plants (meaning rust is more of an aesthetic problem). So your plant is not dying unless what you are/were seeing is something else.
But I understand the need to eradicate rust anyway! Years ago, I finally tracked down where I could locally find a variety of Oakleaf Hydrangea that I wanted and all the samples had rust. They wanted full price, no discounts due to the rust fungal infection so I did not buy. For some strange reason, Smooth hydrangeas like yours "appear" unusually susceptible to rust amongst all hydrangeas.
Avoid overhead watering as a way to minimize the chances of getting rust. Delay sprinklers closer to sunrise. Replace old mulch with new mulch in heavy infestations. Remove plant debris (stems, leaves, blooms) and make sure the soil is not soggy often as this makes the environment moist and nice for the fungi. Remove dead wood and in some cases, live wood to improve air flow (which dries out the area and lets sunlight in). If good sanitation practices do not help (may take a few years of following them to see an improvement), feel free to try fungicides with the following active ingredients: azoxystrobin, kresoxim methyl, mancozeb, myclobutanil, oxycarboxin, propiconazole, triadimefon or trifloxystrobin.
This time of the year, some leaves will turn colors that included red, oranges, yellows and dark greens (almost black) as a result of late frost damage. I thought that may be what you saw. I looked in the picture but, I did not observe frost damage in any of the leaves still on the plant.