For what percentage of the earth's history has there been permanent ice?
As has been abundantly said in the comments and on meta, there is no proper answer to this question in the current state of knowledge.
But indeed we can at least check if we can come up with a rough estimate (and thus try to see from where this 20% estimate comes from).

Let's first look at the main known glaciations:


The Current one: there is indeed a permanent ice sheet on the East Antarctic continent since, presumably, the early Oligocene (i. e. 35Ma, see e. g. DeConto &amp; Pollard 2003). There is considerable dispute on the exact timing of the onset of the EAIS but we're talking here about differences of &lt;10Myrs, i. e. &lt;0.25% of Earth history, so we can ignore for now this difference.
The Karoo ice age: the Carboniferous-Permian glaciation is thought to have spanned from the Mississipian (ca. 360Ma, Buggish et al. 2008) to the Sakmarian (ca. 290Ma; Korte et al. 2008), giving us a ca. 70Myr interval. However some studies have shown (e. g. Fielding et al. 2008) that it was most probably an alternance of glacial and nonglacial climate rather than a continuous glaciation, meaning that permanent ice was probably present for way less than 70Myr.
The Ordovician glaciation: it is thought to have started between the late Katian and the early Hirnantian (ca. 445Ma) and to have ended either before the Silurian (see e. g. Finlay et al. 2010) or at the beginning of the Silurian (ca. 440Ma; see e. g. Cooper &amp; Sadler, 2012). Hence an interval of 1 to 5 Myr. This one has been studied extensively as it is thought to be associated with one of the 5 major mass extinctions of the Phanerozoic (see the whole Sepkoski corpus).
The Cryogenian: two glaciations are thought to have marked the Cryogenian (see e. g. Shields-Zhou et al. 2012), the Sturtian (ca. 720 to 660Ma) and the Marinoan glaciations (ca. 650-635Ma), thus accounting for 75 Myr.
The Huronian glaciation lasting presumably from 2.45Ga to 2.22Ga (see a small review in Van Kranendonk, 2012). The issue here being that the accuracy of paleoproterozoic event datation does not really allow to go much more into the details as this (both because of the extreme scarcity of the data and the relative low resolution of the dating techniques). Leaving us with a glaciation (or more probably a series of glaciations) that could have lasted up to 230Myr.


To this, we can add various minor glaciations that are still highly debated such as the Late Devonian or the Middle to Late Jurassic (e. g. Dromart et al. 2003). Whether of not they indeed occur, they hardly account for much of Earth History when aggregated so we can ignore them safely for the purpose of a rough estimate.

This leads us to 35 + 70 + 5 + 75 + 230 = 415 Myr which equates to ~ 9 % of Earth History. Which is still far off 20% and I doubt that the minor glaciations put together account for 500Myr. 


Buggish, W., Joachimski, M. M., Sevastopulo, G., Morrow, J. R., 2008. Mississippian $\delta ^{13}C_{carb}$ and conodont apatite $\delta ^{18}O$ records — Their relation to the Late Palaeozoic Glaciation. Palaeogeography, Palaeoclimatology, Palaeoecology, 268: 273-292.
Cooper, R. A., Sadler, P. M., The Ordovician Period. In Gradstein et al. 2012, The Geologic Time Scale 2012: 489-523.
DeConto, R. M., Pollard, D. 2003. Rapid Cenozoic glaciation of Antarctica induced by declining atmospheric $CO_2$. Nature, 421: 245-249.
Dromart, G., Garcia, J.P., Picard, S., Atrops, F., Lécuyer, C., Sheppard, S.M.F., 2003. Ice age at the Middle–Late Jurassic transition? Earth and Planetary Science Letters, 213: 205-220.
Fielding, C. R., Frank, T. D., Birgenheier, L. P., Rygel, M. C., Jones, A. T., Roberts, J., 2008. Stratigraphic imprint of the late Palaeozoic ice age in eastern Australia: A record of alternating glacial and nonglacial climate regime. Journal fo the Geological Society, 165: 129-140.
Korte, C., Jones, P. J., Brand, U., Mertmann, D., Veizer, J. 2008. Oxygen isotope values from high-latitudes: Clues for Permian sea-surface temperature gradients and Late Palaeozoic deglaciation. Palaeogeography, Palaeoclimatology, Palaeoecology, 269: 1-16.
Shields-Zhou, G. A., Hill, A. C., Macgabhann, B. A., 2012. The Cryogenian Period. In Gradstein et al. 2012, The Geologic Time Scale 2012: 393-411.
Van Kranendonk, M. J., 2012. A Chronostratigraphic Division of the Precambrian. In Gradstein et al. 2012, The Geologic Time Scale 2012: 299-392.