I am wondering if the loss of vision or hearing early in life (say, before the age of 14 years) affects cognitive abilities later in life? I would imagine that as a group, early-blind or early-deaf people may tend to receive less education than the average healthy individual with normal sight and hearing skills? Given that most IQ tests rely on education-related subjects, would it be fair to conclude that sensory-deprived people, on average, may have lesser IQ, not because of their cognitive abilities per se, but because they tend to receive less education?
This is a really neat question.
A strong predictor of cognitive ability is one's environmental enrichment, or the stimulation of the brain in its physical and social surroundings. Those with sensory deprivation often have less success with social situations and self-esteem, as well as (presumably) less sensory input coming in. The implication is that lack of sensory stimulation during neurodevelopment can impair cognitive development.
This is linked to education in the sense that the educational environment typically provides a cognitively stimulating environment for children to grow in. In that sense, the quality of the educational environment -- and its associated opportunities for engagement in higher-level cognitive activities -- is another factor that predicts cognitive development. 
Interestingly enough, studies have shown that environmental enrichment can correct and rehabilitate the effects of sensory deprivation. One study  showed that physical exercise and an enriched environment actually helped to offset the effects of "dark-rearing" in rats.
Independently of environmental enrichment, the relationship between education and cognitive ability is not well-known. There are studies that suggest that cognitive ability early in life can predict one's success in school, and there is a strong correlation(r~.6-.8) between early childhood IQ and the level of education that the child will end up pursuing. And education certainly contributes to crystallized intelligence, which is the product of education and culture. Both fluid and crystallized intelligence are correlated with each other, thus factoring into one's general intelligence. Regardless, it is fairly well established that cognitive ability predicts success in school, but it is not clear how level of education affects overall cognitive ability.
But perhaps moreso than education is the weight of individual differences in the face of sensory deprivation. For example, certain personality traits are moderately correlated with cognitive ability. Self-efficacy, which is the general feeling that one can succeed in any circumstance, is correlated at around .22. On the Big 5, Openness to Experience is correlated at around .20. But it is important to note that these traits surely predict one's response and ability to cope and adapt to a traumatic event such as total deprivation of the senses (blindness, deafness, etc.) in early development. After all, it is clear that sensory deprivation can be a traumatic life event for individuals, particularly those who are seeing-impaired. To quote from the abstract of this study:
Blindness and sight restoration have been reported to induce both temporary and longer term psychopathology, usually followed by psychosocial readjustment. However, in some cases, readjustment may not occur and suicide may result...When compared with a hearing-impaired control group, impaired sight alone can acutely affect otherwise psychologically healthy individuals.
Given that certain traits that are linked to readjustment are also linked to intelligence, it may be the case that sensory deprivation has a higher impact of long-term cognitive ability in those who have a reduced capacity to begin with, relative to those with higher intelligence and natural ability.
So my informed conclusion would be that yes, sensory deprivation may affect cognitive abilities -- from an educational standpoint, a social standpoint, and a reduction in early stimulation (particularly during the critical period). The overall detrimental impact on these abilities may be relative to the existing intelligence of the person (or the even the existence of traits that are linked to intelligence).
 Wilson R, Barnes L, Bennett D (August 2003). "Assessment of lifetime participation in cognitively stimulating activities". J Clin Exp Neuropsychol 25 (5): 634–42.
 Argandoña, Enrike G, Harkaitz Bengoetxea, and José V Lafuente. “Physical Exercise Is Required for Environmental Enrichment to Offset the Quantitative Effects of Dark-Rearing on the S-100β Astrocytic Density in the Rat Visual Cortex.” Journal of Anatomy 215.2 (2009): 132–140. PMC. Web. 25 Aug. 2015.