I built the Lakeview manor earlier in my current game and just started building the Windstad manor. I've had problems getting sawn logs. The mill operator in Morthal has no dialogue option to buy logs from him and neither did the mill operator in Dragon's Bridge. The mill operator in Riverwood was no where to be found, so I don't know if I could get logs there. In the end, the only place that I could buy logs was in Falkreath, where I had bought them for my first home, Lakeview Manor. It doesn't make sense that I would have to trek half way across Skyrim to buy logs.

My question is this: Shouldn't I be able to buy logs from any mill, or at least from more places than just Falkreath?

You should be able to buy them at any mill. At first when I built my very first home (Falkreath) I though that I had to buy logs from a nearby mill. Not the case. Ive gone as far north as Solitude to buy logs for my Falkreath home, and thats just because I happened to be trekking around that area.

The mill operator in Riverwood (Hod) may have been killed in some random attack - try waiting there for a few hours to see if he shows up.

But the easiest way to deal with it is to hire someone to be your steward at Winstaad Manor, and have him/her buy lumber for you.

I usually just start the mill up to get Hod out of his house, or chop some wood. For a mill owner you are not friends with, you could always try selling them some wood to start things off. If you get tired of chasing logs and are rich with a house steward, you can just get the steward to buy the logs. Does not matter which steward or which house they are at, the one pile of logs is for all three houses. So of you run out of logs for Windstad, you can run down to Lakeview Manor and ask your steward down there to order more logs. I would not take an existing steward to a new house in case something goes wrong and they end up attached to the wrong house, or you forget and make them steward for both houses. They can only be steward for the first house.

If you already have enough of the house built it would be easier just to go find a steward for that house as Gator Country suggested.

Yup - the pile of logs, unique among your construction materials, is shared among all your houses. If you had 50 logs remaining in Lakeview, the moment you buy Windstad you should have the same 50 logs there (not sure if it adds on the initial free logs if you did that, it probably should). A certain vampy chick near Falkreath has supplied all my logs for pretty much all my Hearthfire houses, and she apparently delivers all the way to Heijarchen, bless her, even though she claims she only supplies Falkreath and, until lately, Helgen.

Are you sure you're talking to the correct NPC? http://www.uesp.net/wiki/Skyrim:Thonnir is the owner of the mill in Morthal, not http://www.uesp.net/wiki/Skyrim:Jorgen, although Jorgen is there more of the time. If you've done Laid to Rest, Thonnir will even let you cut your own logs for free.

For some strange reason, that mill doesn't sell logs to the public, so you can't buy logs from Dragon's Bridge. You can buy logs from Solitude Sawmill, though. Talk to the orc employee. Unfortunately, you cannot cut your own logs for free here because there is no option to befriend the orc, so you'll have to pay full price.

Yes. As Aussie mentioned, Hod sometimes hides in his house. Running a log through the mill will make him come out. This is true for any mill owner (except Dragon's Bridge). That might be the problem you're having in Morthal, as well--Thonnir may be stuck in his house.