It's a complicated topic, because we all need food on the table. I will say it depends. It mainly depends on how much I'm paid for the task, if it's in the high end, it's usually expected that I can spend my own time to learn new things - these tasks are fixed price though. If it's paid per hour, and not a lot, I expect them to pay for whatever resources I need to put into the job, even if it's a new tool that I can't avoid using.
It's like if you pay for the business class, everything is included, if it's the discount class you pay for everything.
But to add to that, I would never spend something without consulting my client first and I always supply free support to make sure the client can use what I made and is satisfied.