Why does it not evaporate? The answer is simple: the vapor pressure of water at very low temperatures is far below even the applied pressure of the vacuum of deep space.

For more information, see this site:
Water in Space More Abundant than Expected

Source: Saturation vapor pressure formulations

The point is that the vapor pressure of water ice at 3 kelvins is far LOWER than 10-16 mbar. In fact, it is too low to be measured directly, so it must be extrapolated from measurable data using techniques from Physical Chemistry

http://cires.colorado.edu/~voemel/vp.html
Goff Gratch equation (considered the most accurate over the entire range used)
Log10(P) = -9.09718 (273.16/T - 1) - 3.56654 Log10(273.16/ T) + 0.876793 (1 - T/ 273.16) + Log10(6.1071)
with T in [K] and P in [hPa]
1 hectopascal [hPa] = 100 Pa = 1 mbar

Here are some typical values of the log10( vapor pressure of ice) at very low temperatures using the Goff Gratch equation. This is the log10 of the pressure, not the pressure itself:

T in kelvins · log10(Pressure) in hPa (1 hectopascal [hPa] = 100 Pa = 1 mbar )
1 · -2482.919
2 · -1239.355
3 · -824.566
4 · -617.042
5 · -492.450
6 · -409.338
7 · -349.936
8 · -305.358
9 · -270.665
10 · -242.894
11 · -220.159
12 · -201.201
13 · -185.151
14 · -171.386
15 · -159.449
16 · -148.998
17 · -139.772
18 · -131.565
19 · -124.219
20 · -117.603
21 · -111.614
22 · -106.166
23 · -101.190
24 · -96.625
25 · -92.424
26 · -88.543
27 · -84.948
28 · -81.608
29 · -78.496
30 · -75.591
31 · -72.871
32 · -70.320
33 · -67.922
34 · -65.665
35 · -63.535
36 · -61.522
37 · -59.617
38 · -57.812
39 · -56.098
40 · -54.469
41 · -52.919
42 · -51.442
43 · -50.032
44 · -48.687
45 · -47.400
46 · -46.169
47 · -44.989
48 · -43.858
49 · -42.773
50 · -41.731
51 · -40.729
52 · -39.765
53 · -38.837
54 · -37.943
55 · -37.081
56 · -36.249
57 · -35.447
58 · -34.671
59 · -33.922
60 · -33.197
61 · -32.496
62 · -31.817
63 · -31.159
64 · -30.521
65 · -29.903
66 · -29.303
67 · -28.721
68 · -28.156
69 · -27.607
70 · -27.074
71 · -26.555
72 · -26.050
73 · -25.559
74 · -25.081
75 · -24.616
76 · -24.163
77 · -23.721
78 · -23.291
79 · -22.871
80 · -22.461
81 · -22.062
82 · -21.672
83 · -21.291
84 · -20.920
85 · -20.556
86 · -20.202
87 · -19.855
88 · -19.516
89 · -19.184
90 · -18.860
91 · -18.542
92 · -18.232
93 · -17.928
94 · -17.630
95 · -17.339
96 · -17.053
97 · -16.774
98 · -16.500
99 · -16.231
100 · -15.968
101 · -15.709
102 · -15.456
103 · -15.208
104 · -14.964
105 · -14.725
106 · -14.490
107 · -14.260
108 · -14.033
109 · -13.811
110 · -13.593
111 · -13.379
112 · -13.168
113 · -12.961
114 · -12.758
115 · -12.558
116 · -12.361
117 · -12.168
118 · -11.978
119 · -11.791
120 · -11.608
121 · -11.427
122 · -11.249
123 · -11.074
124 · -10.902
125 · -10.732
126 · -10.565
127 · -10.401
128 · -10.239
129 · -10.080
130 · -9.923
131 · -9.768
132 · -9.616
133 · -9.466
134 · -9.318
135 · -9.172
136 · -9.029
137 · -8.887
138 · -8.748
139 · -8.610
140 · -8.475
141 · -8.341
142 · -8.209
143 · -8.079
144 · -7.951
145 · -7.824
146 · -7.700
147 · -7.576
148 · -7.455
149 · -7.335
150 · -7.217

Note that not until 100 kelvins is the pressure significant.