Ok so i'm starting on my hearthfire house building and seeing that i'm frugal about how much I spend on iron or any type of thing it ore i wanna know how long does it take for a vein like iron to replenish itself?

In a cleared dungeon it takes 30 days if you are away from it.

how about un-cleared mines like iron-breaker?

I think it's 10 days.

And incase you want to find where to find ore viens of a specific type, click on the links corresponding to the ores, http://www.uesp.net/wiki/Skyrim:Mining

Edit: or rather viens in a specific area, the links in the page linked above will take you to a table, listing locations and how many viens are there.

I'd greatly encourage you to abandon that reasoning, though. Building a single house requires insane amounts of Iron. Hundreds upon Hundreds. The time it would take you to scout out enough Iron Ore veins to complete your house may take a couple IRL days, not to mention you'd most likely have to wait the 30 day period for them to refill a couple times. Gold is super easy to obtain, especially if you use Alchemy, and not as a skill. Just picking up every ingredient you find, making potions, and selling them.

It took me a 2-3 hours to complete Lakeside while buying all my needed Iron and materials, only missing the animal plaques. That's a very tedious amount of time for something that most people, including myself, use to store items in. In fact, I've only used Hearthfire 3-4 times, only making Lakeview, and not always an entire house(Sometimes just the base shack thing). I usually just save Gold and Time and buy Breezehome or Proudspire Manor.

But I guess I got off topic.

www. uesp. net/wiki/Skyrim:Respawn

I guess I can't post links. I hope I don't get banned, but there's a page explaining it.

Do not worry posting links is not prohibited, as far as i am aware, i havent been banned yet, and i have posted many links.

Edit: also to note, it is very easy to gain large sums of money very easily, especially if you complete no stone unturned, you find gems nearly everywhere, containers that is, and the quest is tedious, at worse.

Too long to make it worth your while.

Most merchants sell iron ore/ingots that mining should only be done if you've tapped them out. All shops will replenish their stock in 3 days, so it's easier to buy them.

If you're worried about money, don't be. Instead, sell back weapons and armor in exchange for the iron ingots/ores.

Oh, and just in case you're about to spend money on logs: don't. Instead, head to any mill with an owner, who'll usually tell you to chop wood for gold. Cut some wood, then sell it back to the owner. At this point, tell them you want to buy logs. Another option will then show up about you cutting your own.

When you do this, the logs are free and you get 10 sawn logs for every log you cut. It's a bit boring to watch the animations, but you can grab 200 sawn logs within a real-time hour.

By the way: I find selling gems to be much easier than selling weapons and armor. They're lighter to carry and you get a better return. Just a head's up if you intend to mine ores.