Glad you asked this question!  This is a subject I have become quite interested in for a reason I will explain after answering your question. 
Often the best way to id birds with abnormal plumage coloration is by the company they keep, especially with birds that normally appear in flocks.  "Loner" birds can be more difficult.  So...is it hanging out with other house finches?  
Your probable house finch is not actually albino but rather leucistic.  Albinism is a condition that can occur in all birds and mammals resulting from a complete lack of pigmentation.  Therefore Albino birds have no coloration at all; no colored spots & the legs & eyes are pink (because there is no color present, the pink color comes from the circulating blood).  And there is no such thing as a "partial albino" though this is a commonly used term.  A creature is either albino or it isn't.  No half-ways.  Leucistic is the term most scientists use to describe an animal that is missing some, but not all pigmentation.  It is a plumage abnormality created by a lack of melanin from some or all of the feathers.  Pigmentation is created from melanin (brown & black colors) & carotenoids (red & yellow colors).  Melanins are enzymes, carotenoids are ingested.  Leucism is a genetic abnormality and does not affect the carotenoid pigments.  Leucistic birds have dark eyes.
I have seen several all white or mostly white house finches over the years so I think this is not an uncommon occurrence among house finches.  (Some species seem to have this occur more often than others.  Red-tail hawk, blue jay and Am. robin are some others that come to mind.)  One was an absolutely gorgeous bird that was completely snow white with only black eyes, bill & legs. I could only assume it was a house finch & not a goldfinch, house sparrow or something else because it was always in the company of other house finches.  I also surmised it was a female because of the complete lack of color....a male would show some carotenoid pigment.
The reason I have become so interested in leucistic birds comes from the leucistic female cardinal we have hosted at our feeders for the past 6 years!  When we first observed her one winter she was a mostly normally colored bird but sporting a few pinkish feathers in her wings, tail and body and a very white "collar" around her neck.  After she molted, the collar was wider and there were a few more white and pinkish feathers.  Every year thereafter, she has become whiter and whiter until she is now a pure white bird sporting a somewhat pink crest, and pink wing & tail feathers.  Beautiful bird.  And, contrary to common belief that leucistic birds are not prone to finding a mate and successfully raising young, she has done both for at least 3 years.  It is also generally felt that albino and leucistic birds do not survive long as they make such easy prey.  Yet our 'Luci' has managed to hang in there despite the numerous feral cats and other more naturally occurring predators present.
I know this is a pretty long answer to a pretty simple question but I do find abnormally colored birds fascinating.  I hope others do also.
Laura Dornan, Stark Co.

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