I suggest you get it dealt with now. It will be easier to do now rather than later on. Plus, if something needs doing later, you will be really dreading having to fight with it then.
Heat, pressure, mega hammer, penetrating oil etc.
Put the nut backwards on the threads of the axle, down to so that the threads are just lower than the nut. Then wail away. If you heat the spindle, you may damage the bearing, but you may have to anyways.
If you can find a bearing puller/press made for removing wheel bearings on the car, you may be able to press it out. Then again, you may have to just get new spindles and axles. I came close on a customers car.
I actually fractured the 1" diameter tool steel Snap-on puller I was using!! I left it sit with pressure on it all thru lunch and it FINALLY let go, but under tension I could see an axial crack along the threaded shaft of the tool. I would not have believed it. Then again, I was using a 3/4" air impact on it
That thing is like a 40mm Bofors. BUM!BUM!BUM!BUM! Shakes the whole body when using. If you don't have access to that, again, I suggest just getting some spindles and axles.