Mine did the same thing when it was new (2004). It would shut off before it built oil pressure. I switched to 5-40 Rotella, made no difference so I had my dealer make a farm call and here is what he found.......
On the front of the engine, right behind the lower pulley is a cap (on the left side facing forward). Under that cap there is a spool valve the controls oil pressure. The bore on my spool valve had a tiny burr in it and the spool was hanging on the burr just enough that the spool wouldn't shuttle consistently. In my case because the tractor was new, it went back to my dealer and under warranty, they replaced the entire front timing case.
I think they could have taken a piece of crocus cloth and smoothed the burr and that would have eliminated the issue but because it was new, Kubota had them replace it.
Haven't had a lick of trouble since then.
My suggestion is pull the plug and inspect the spool and bore and if there is a burr, use some crocus cloth on it to smooth it out. That shuttle spool has to move freely or the engine won't build pressure fast enough (under 5 seconds) and it shuts the engine down.
There is a coil spring in there, make sure you put the spring back in the way it comes out. That spring controls the oil pressure.
Don't need to drain the oil, a tiny bit will come out, that is all.
The service tech took mine apart in the farm yard but when he found the burr, the tractor went back for the case replacement. He agreed that it could have been smoothed out but being new, it was gonna be a Kubota deal..
Not hard to get to. If you lay under the tractor and look up, it's right in front of the oil pan between the pan and the pulley.
It gets cold here as well and I use the tractor for snow removal si I stick with the 5-40 because it cranks easier. No electricity in the barn to plug a block heater in to.
Hope that helps.