A voltage divider is not an appropriate replacement for a voltage regulator if you want to draw any significant amount of power. This is because the output is high impedance. The source impedance will be equivalent to the parallel combination of the two resistors. Using the values you list in your post, 68K and 340K, the output impedance would be around 56.6K. The maximum current you can draw from that is 10V/56.6K = 176 microamps...by shorting the output to ground. And if you want the output to be, say, within 1% of 10 volts, then you can only draw 1% of that current, or less than 2 microamps. If your circuit only needs 1 microamp, then it will work fine, although the divider is going to pass 12/(340+68) = 29 microamps directly to ground, resulting in a power efficiency of about 1*10/((29+1)*12) = 2.8%. And that efficiency will be the same if you use smaller resistors so you can draw more current - for instance if you drop down to 340 ohms and 68 ohms and draw 1 mA instead of 1 uA, the efficiency is still 2.8%.
So yeah, if you want to supply power, use a voltage regulator, that's what they're made for. Also, if you're trying to regulate 12V down to 10V, you'll want a regulator that can deal with that relatively small 2V difference. You'll have to get a relatively decent low-dropout regulator (LDO).