I am able to create random correlated standard normal draws using PROC IML and feeding it a correlation matrix and a vector of means=0 (see the code below)
 
*Create Lower Triangular Correlation Matrix;
DATA Have_Matrix;
INPUT C1 C2 C3 C4;
DATALINES;
1	.7	.2	0
.7	1	.4	.5
.2	.4	1	.3
0	.5	.3	1
;RUN;
*Create a vector of Means=0;
DATA Have_Means (Drop=i);
DO i = 1 TO 4;
	Mean = 0;
	OUTPUT;
END;
RUN;
*Create the Correlated Random Draws;
PROC IML;
USE Have_Matrix;
READ ALL VAR _NUM_ INTO CovMatrix;	*Symmetric Covariance Matrix;
USE Have_Means;
READ all VAR _NUM_ INTO Mean;
N = 1000;							*sample size;
X = RandNormal(N, Mean, CovMatrix);	*1,000 x 4 Correlated Std Normal Draws;
CREATE Want FROM X; APPEND FROM X; CLOSE Want;
QUIT;
How do I do this using a Student's T distribution? (I believe the above code defaults to Gaussian? I could be wrong about that so please correct me if I am misinterpreting)