I was just wondering about where I could find ores for smelting, particularly steel ores

In mines

i was wondering to mined ores fill up again after some time, i did check quicksilver mine after a while when i mined it dry, there was nothing.

Mines take about a month of ingame time to refill their ores.

Okay, where do I find mines, and do I need a pickaxe to mine in them?

Go and explore, there is a mine in Dawnstar though, to start you off and yes you need a pickaxe.

You need a pickaxe to mine ores, and mines usually show up on the map as an icon with two crossed pickaxes. However, you can also find ores in other locations (like caves), and even on normal terrain. For example, just outside of whiterun there's two corundum ore veins. And the halted stream camp is chuck full of iron ore veins.

Oh and to make steel ingots you need one corundum ore and one iron ore.

Oh and last but not least, there's also mines that don't show up on the map, like the two mines in dawnstar and the mine in markath.

Yes. Also instead of activating the ore and watching the sequence play out ou can actually take out you pickaxe and swing at the wall. If you have 2 pickaxes you can dual wield and do it faster.

I carry around the pick ax for a while don't find any ores. Drop it because I need the weight loss. Next cave I enter has ore to mine with no ax. Repeat.